Environmental Performance and Bank Productivity: A Cost-Efficiency Decomposition Approach Using VRS Cost Malmquist Analysis

Abstract

This study examines environmental performance and bank cost productivity using a VRS Cost Malmquist decomposition framework. Using annual data from 18 listed Taiwanese banks (2017–2023, 18 banks × 6 years = 108 bank-transition observations), the framework integrates input and output quantities with input prices in a cost-based productivity system. CMPI is decomposed into pure technical efficiency, technological change, allocative efficiency, price effects, and cost scale efficiency, thereby revealing channels of cost productivity change. The reported pooled OLS estimates suggest negative associations between environmental performance and CMPI, pure technical efficiency change, technological change, and allocative efficiency change. These associations remain exploratory because serial-dependence and finite-sample inference concerns remain unresolved. The decomposition provides a more detailed description of productivity variation without establishing causal mechanisms.

1. Introduction

1.1. Research Background and Motivation

Global climate change and ecosystem destruction threaten human survival. Root causes include rapid industrialization since the Second Industrial Revolution, which generated severe pollution and intensified climate change. In response, major industrialized countries signed the Kyoto Protocol in 1997, establishing the first framework for reducing carbon emissions. This was strengthened in 2015 by the Paris Agreement, which outlined strategic actions and emphasized sustainable development as a core principle [1]. Environmental (E), Social (S), and Governance (G) have since emerged as the three pillars of corporate sustainability, collectively termed ESG [2,3]. Among these, environmental protection is a key measure of sustainability in the banking sector.

Governments and capital markets worldwide stress transparency in ESG disclosures [4]. Although Taiwan is not a signatory to the Paris Agreement, it remains integral to global supply chains and capital markets and actively responds to sustainability trends [5]. Since 2017, Taiwan’s Financial Supervisory Commission (FSC) has enforced the Green Finance Action Plan, requiring banks to adopt ESG practices and climate risk standards by 2023 [6]. The environmental dimension includes carbon management, green finance, and risk control [7]. Although previous studies have examined the association between ESG performance and bank profitability, efficiency, and risk, aggregate financial performance measures provide limited information about the specific operational channels underlying these relationships. Banks may achieve similar financial outcomes through different combinations of technical efficiency, technological change, resource allocation, input-price management, and scale. Consequently, examining aggregate financial performance alone may obscure how environmental performance is associated with the underlying productivity structure of banking operations.

1.2. Problem Statement and Research Objectives

Previous studies report mixed evidence on the relationship between ESG performance and bank outcomes. Shakil et al. (2019) [8] and Nizam et al. (2019) [9] find positive effects of environmental performance, while Li and Deng (2025) [10], Bătae et al. (2020) [11] and Bressan (2024) [12] report insignificant or negative relationships. In Taiwan, research has primarily focused on social and governance dimensions, with limited attention to environmental performance [13]. Although the Cost Malmquist Productivity Index (CMPI) has been applied to banking, few studies integrate VRS cost-frontier analysis, CMPI decomposition, and ESG variables [14,15,16]. This study addresses this gap by decomposing CMPI into technical efficiency, technological change, allocative efficiency, price effects, and cost–scale efficiency using Taiwanese banking data. Accordingly, the study asks: RQ1: Is environmental performance associated with bank cost productivity? RQ2: Which cost-efficiency components are associated with environmental performance? RQ3: What inference limitations qualify the observed associations?

2. Literature Review

This section divides the literature review into two parts. The first part reviews previous studies on how the development of green finance affects the operational performance and risk levels of financial institutions. The second part explores recent advancements in methods for assessing changes in productivity and efficiency within financial institutions.

2.1. Environmental Performance and Banking Productivity

Environmental, social, and governance (ESG) performance has become increasingly important in evaluating financial institutions. Environmental performance may affect banks’ operational efficiency, resource allocation, technological adoption, and cost management [17]. However, its effects may differ across institutional settings and performance measures. Rather than directly improving profitability, environmental performance may influence bank productivity through operational and organizational channels. Unlike physical production firms, banks primarily transform information, financial capital, employee time, and information-processing capacity into financial services. Accordingly, environmental performance may affect productivity when environmental and climate-related considerations are incorporated into credit assessment, risk management, information processing, and resource allocation [18].

(1)

Environmental performance and operational/technical efficiency.

The first mechanism concerns Pure Technical Efficiency Change (ΔPTE), which reflects how effectively banks use existing inputs under available technology. Environmental and climate-related considerations may require banks to collect information on borrowers’ environmental exposure, sector characteristics, transition risks, and compliance conditions [17]. Integrating such information into existing credit-screening and monitoring procedures may standardize information collection and reduce duplicated or fragmented assessments. In banking, operational waste therefore includes redundant information processing, unnecessary manual procedures, repeated risk assessments, and inefficient use of employee time. Embedding environmental management into established credit and risk management processes may improve internal information processing and risk control, thereby enhancing technical efficiency [19].

(2)

Environmental performance and technological change.

The second mechanism concerns Technological Change (ΔT), which captures shifts in the feasible input–output frontier rather than improvements in efficiency under existing technology. In banking, environmental and climate risk management requires the integration of borrower emissions, sectoral transition risks, and the environmental characteristics of financed activities into credit assessment and monitoring. These requirements can exceed the capabilities of conventional information systems, creating incentives for banks pursuing stronger environmental performance to invest in new data-processing and decision-support technologies [18].

Huang et al. (2026) [20] find that AI application reduces carbon emission intensity in Chinese manufacturing enterprises through green innovation, improved total factor productivity, and stronger analyst monitoring. Their study examines technological capability as an antecedent of environmental improvement and provides a cross-industry reference for the connection between digital capability, environmental management, and productive efficiency. Extending this reasoning to banking, we propose that environmental management requirements may stimulate technology investment by increasing demand for integrated environmental information and continuous monitoring.

Potential applications include AI-driven models that incorporate environmental and transition risk information into credit assessment, block chain-enabled systems that support traceable green-credit records, and digital carbon-accounting platforms that standardize emissions-data collection and reporting. Where these investments expand analytical capacity and automate previously labor-intensive tasks, they may enable banks to provide comparable financial services with fewer inputs, thereby shifting the frontier and potentially improving cost productivity. Unlike ΔPTE, which concerns better use of existing technology, this channel concerns changes in technological capability [21]. However, implementation costs and data limitations may constrain these benefits. These applications therefore represent theoretical mechanisms; the present study examines the association between environmental performance and ΔT without directly measuring technology adoption or establishing causality.

(3)

Environmental performance and allocative efficiency.

The third mechanism concerns Allocative Efficiency Change (ΔAE), which reflects how effectively banks allocate inputs across alternative uses. Incorporating environmental risk into lending decisions may influence portfolio composition, credit-screening intensity, monitoring resources, and the allocation of financial, human, technological, and organizational resources. For example, banks may direct greater analytical and risk management resources toward environmentally sensitive sectors or portfolios [19]. Thus, environmental performance may improve productivity not only by reducing input use but also by changing where and how existing resources are deployed.

This study examines three components related to bank productivity, representing different dimensions of bank productivity: ΔPTE focuses on the efficiency of existing processes; ΔT focuses on improvements in information and decision-making technologies; and ΔAE focuses on resource allocation across various bank operations [19,20,21,22]. Examining these components related to bank productivity provides a banking-specific theoretical basis for linking environmental performance with cost Malmquist decomposition. Importantly, these components are theoretical pathways, not direct evidence of specific organizational practices. Because this study uses the Environmental Dimension Score (EDS) to measure environmental performance and the decomposed cost Malmquist index to measure productivity, the empirical analysis examines statistical correlations rather than directly identifying specific green credit programs, environmental risk models, or carbon accounting systems. Therefore, ESG performance may affect banks through multiple pathways rather than directly improving accounting profitability. This issue is particularly relevant to the Taiwanese banking industry due to its stringent operating environment regulations and the changing costs of labor, capital, and financing. Under these conditions, improvements in environmental performance may be more evident in input–output conversion efficiency and cost control. As shown in Table 1, the productivity-based perspective provides a useful framework for examining the economic impact of Taiwan’s banking sector’s environmental participation.

Table 1. Framework for Environmental Performance.

	Frame	Illustration	References
1	Environmental performance → operational efficiency	Environmental management may reduce resource waste and improve internal operational processes	[1,4]
2	Environmental performance → technological change	Environmental commitments may encourage adoption of digital, energy-efficient, monitoring, and risk management technologies.	[2,10]
3	Environmental performance → allocative efficiency	Environmental considerations may alter the allocation of financial and organizational resources toward more efficient uses.	[1,3,10]

Nevertheless, most ESG studies focus on financial and risk outcomes, with limited attention to how environmental performance affects cost productivity over time. This study addresses this gap by integrating ESG dimensions into a cost-based productivity framework, examining technical efficiency, technological change, allocative efficiency, price effects, and scale effects.

2.2. DEA-Based Productivity Measurement

Data Envelopment Analysis (DEA) is a non-parametric method for evaluating the relative efficiency of decision-making units (DMUs) with multiple inputs and outputs. By constructing an empirical production frontier from observed data, DEA is particularly suitable for banking applications. Caves et al. [23] introduced the Malmquist productivity index, which Färe et al. [24] later developed into a DEA-based framework, allowing productivity change to be decomposed into efficiency change and technological change. Ray and Desli [25] extended this framework by incorporating variable returns to scale (VRS), Peykani et al. [26] and Zofío and Lovell [27] further examined scale and technological effects. VRS-DEA is relevant to Taiwanese banks because of differences in operating scale and resource structures. However, conventional Malmquist indices focus mainly on input and output quantities and do not explicitly consider input prices. Since labor, funding, and capital costs can significantly affect banking costs, a cost-oriented framework is needed. This provides the methodological basis for the Cost Malmquist Productivity Index (CMPI).

2.3. Cost Malmquist Productivity Index

The Cost Malmquist Productivity Index (CMPI) extends the conventional Malmquist index by incorporating input prices into intertemporal productivity measurement. Maniadakis and Thanassoulis [28] developed the CMPI framework, allowing productivity changes to reflect technical efficiency, allocative efficiency, technological change, and input price effects. This cost-oriented approach is particularly relevant to banking because changes in labor, funding, and capital prices can affect costs even when input and output quantities remain stable. The framework was later extended to variable returns to scale (VRS) by Yang and Huang [14], who applied it to Taiwanese banks and demonstrated its ability to identify price and scale effects. Yang et al. [16] further applied DEA and CMPI to examine FinTech and banking productivity. Following these developments, this study adopts a VRS cost-frontier framework and decomposes CMPI into five components: pure technical efficiency change (ΔPTE), technological change (ΔT), allocative efficiency change (ΔAE), price effect change (ΔPE), and cost scale efficiency change (ΔCSE). These components are linked to ESG dimensions to identify specific productivity mechanisms associated with environmental performance.

2.4. Research Gap and Analytical Contribution

The preceding literature reveals three methodological gaps. First, ESG studies in banking mainly focus on profitability, risk, and financial stability, with limited attention to specific productivity, examining component-specific associations. Second, conventional DEA-based Malmquist indices are quantity-oriented and may overlook input prices and cost allocation. Third, few studies integrate a VRS cost-frontier framework with ESG dimensions to identify the productivity components associated with environmental performance.

Beyond methodological integration, this study proposes an information-processing and resource-allocation framework linking environmental engagement to distinct dimensions of bank productivity. Environmental practices introduce requirements to collect, interpret, and monitor information on borrowers’ environmental exposure and transition risks. Three theoretically distinct responses may follow. First, integrating this information into existing credit and monitoring procedures may reduce duplicated assessments and improve the use of available inputs, corresponding to ΔPTE. Second, when environmental information requirements exceed existing system capabilities, banks may invest in new analytical and monitoring technologies, corresponding to ΔT. Third, differences in environmental exposure across portfolios may motivate adjustments in the mix of labor, capital, and funding inputs relative to their prices, corresponding to ΔAE. The framework therefore distinguishes better use of existing technology, changes in technological capability, and more cost-efficient input combinations. These are proposed theoretical mechanisms rather than causally identified pathways; the empirical analysis examines whether environmental scores are associated with the corresponding productivity components.

Under the input-oriented cost-index convention adopted in this study, index values below one indicate improvement, whereas values above one indicate deterioration. Accordingly, the proposed association between stronger environmental performance and improved cost productivity implies a negative coefficient on environmental performance. The operational, technological, and resource-allocation mechanisms discussed in Section 2.1 provide the theoretical basis for negative expected associations with CMPI, ΔPTE, ΔT, and ΔAE. By contrast, the direction of the associations with ΔPE and ΔCSE is theoretically less determinate. Environmental engagement does not necessarily reduce input prices or move banks toward the cost-efficient scale. These two relationships are therefore examined as exploratory research questions.

To address these gaps, this study develops an integrated VRS-DEA cost-productivity framework. First, a VRS production possibility set and cost frontier are constructed using DEA-based linear programming. Second, the Cost Malmquist Productivity Index (CMPI) is calculated and decomposed into five components: pure technical efficiency change (ΔPTE), technological change (ΔT), allocative efficiency change (ΔAE), price effect change (ΔPE), and cost scale efficiency change (ΔCSE). Third, these productivity measures are incorporated into panel regression models to examine their associations with ESG performance conditional on the included ESG variables and controls. This framework examines associations with technical efficiency, technological change, allocative efficiency, price effects, and cost–scale efficiency, providing a basis for the directional hypotheses (H1–H4) and exploratory research questions (RQ4–RQ5) below.

H1. 

Environmental performance is negatively associated with the Cost Malmquist Productivity Index (CMPI), indicating improved bank cost productivity.

H2. 

Environmental performance is negatively associated with the pure technical efficiency change index (ΔPTE), indicating improved pure technical efficiency.

H3. 

Environmental performance is negatively associated with the technological change index (ΔT), indicating technological improvement.

H4. 

Environmental performance is negatively associated with the allocative efficiency change index (ΔAE), indicating improved allocative efficiency.

RQ4: 

Is environmental performance associated with price-effect change (ΔPE)?

RQ5: 

Is environmental performance associated with cost–scale efficiency change (ΔCSE)?

3. Research Methods

This study combines CMPI measurement with panel regression to examine the relationship between ESG performance and productivity in Taiwan’s banking industry from 2017 to 2023. A three-stage framework was adopted: (1) ESG and financial data were collected from the TEJ Bank ESG Data archive and compiled in Excel; (2) CMPI and its components were calculated using MATLAB R2023b; and (3) the results were imported into SPSS 22 for regression analysis of associations between ESG dimensions and productivity, conditional on the included controls.

3.1. Data Sources and Variable Selection

In the first stage, data were collected from the Taiwan Economic Journal (TEJ) Bank ESG Data archive for 18 listed Taiwanese banks over seven years (2017–2023). The dataset included EDS, SDS, GDS, LTA, NPR, and the financial indicators required for productivity measurement. Data were screened, coded, and standardized to support consistent CMPI calculation and subsequent regression analysis. CMPI was calculated for six consecutive year-to-year transitions per bank, yielding 108 bank-transition observations rather than 108 annual bank-year observations.

The Environmental Dimension Score (EDS) serves as a composite measure of banks’ environmental performance. It captures multiple aspects of environmental sustainability rather than individual practices such as green-credit procedures, environmental investment, or carbon management. Banks may therefore achieve similar EDS values through different combinations of environmental activities, management practices, and disclosure. Accordingly, the empirical analysis examines conditional associations between overall environmental performance and CMPI and its components. The mechanisms proposed in Section 2.1 provide a theoretical basis for interpreting these associations but are neither directly observed practices nor empirically established causal pathways.

3.2. Cost Malmquist Productivity Index Framework

In the second stage, financial and operational data from the Taiwan Economic Journal (TEJ) were processed using MATLAB to calculate the Cost Malmquist Productivity Index (CMPI) and its components. MATLAB efficiently performs the DEA-based linear programming and intertemporal cost calculations. Using data from 18 listed Taiwanese banks from 2017 to 2023, comprising 108 bank-transition observations, CMPI and component indices were calculated for consecutive periods and used as dependent variables in the third-stage regressions.

3.2.1. Variable-Returns-to-Scale Cost Frontier

To measure intertemporal changes in cost productivity, this study constructs a variable-returns-to-scale (VRS) cost frontier using a Data Envelopment Analysis (DEA) framework. Let DMU_k denote bank k, $x_k^t \in {\mathrm{R}}_{+}^{\mathrm{m}}$ the input vector, $y_k^t \in {\mathrm{R}}_{+}^{\mathrm{s}}$ the output vector, and $w_k^t {\in \mathrm{R}}_{+}^{\mathrm{m}}$ the corresponding vector of input prices in period t. The VRS production possibility set is defined as

$$T_V^t=\left\{\left(x,y\right):\right.x\ge {\displaystyle {\sum }_{j=1}^N}{\lambda }_j^t{x}_j^t, y\le {\displaystyle {\sum }_{J=1}^N}{\lambda }_j^t{y}_j^t, {\displaystyle {\sum }_{J=1}^N}{\lambda }_j^t=1, {\lambda }_j^t\ge 0$$

(1)

The convexity constraint

$${\displaystyle {\sum }_{j=1}^N}{\lambda }_j^t=1$$

(2)

imposes variable returns to scale. The associated VRS cost frontier is defined as the minimum expenditure required to produce a given output vector at prevailing input prices:

$$C_V^t\left(y,w\right)=\begin{array}{c}\mathit{min}\\ x\end{array}\left\{{\omega }^{t^{\prime }}\right.x:\left(x,y\right)\mathsf{ϵ}\left.T_V^t\right\}$$

(3)

This formulation provides the mathematical basis for evaluating changes in R_CE = 1 and productivity between two consecutive periods.

3.2.2. R_CE = 1 and Direction of the Index

For bank k in period t, let the observed cost be

$${\mathit{AC}}_k^t={\omega }_k^{t^{\prime }}{x}_k^t,$$

(4)

and define the VRS R_CE = 1 as

$${\mathit{CE}}_{k,V}^t={\displaystyle \frac{C_{k,V\left(y_k^t,{\omega }_k^t\right)}^t}{{\omega }_k^{t^{\prime }}{x}_k^t}}, 0<{\mathit{CE}}_{k,V}^t\le 1$$

(5)

A value of ${\mathit{CE}}_{\mathit{k},\mathit{V}}^{\mathit{t}}$ closer to one indicates that the observed input allocation approaches the minimum-cost frontier, whereas a lower value indicates a larger deviation from the cost frontier.

To illustrate the direction of cost-efficiency change, the following ratio compares contemporaneous cost efficiencies between periods t and t + 1:

$$R_{\mathit{CE},k}^{t,t+1}={\displaystyle \frac{{\mathit{CE}}_{k,V}^t}{{\mathit{CE}}_{k,V}^{t+1}}}$$

(6)

Under this cost-efficiency-ratio convention, the interpretation is reversed relative to the conventional productivity-growth orientation of the standard Malmquist index. Specifically,

$$R_{\mathit{CE},k}^{t,t+1}>1⟹{\mathit{CE}}_{k,V}^t>{\mathit{CE}}_{k,V}^{t+1}$$

(7)

indicating a deterioration in R_CE = 1 from t to t + 1.

Conversely,

$$R_{\mathit{CE},k}^{t,t+1}<1⟹{\mathit{CE}}_{k,V}^t<{\mathit{CE}}_{k,V}^{t+1}$$

(8)

A ratio below one indicates an improvement in contemporaneous cost efficiency. A ratio equal to one indicates no change in contemporaneous cost efficiency.

A ratio below one indicates an improvement in contemporaneous cost efficiency, whereas a ratio equal to one indicates no change, as shown in Equation (9).

$$R_{\mathit{CE},k}^{t,t+1}=1$$

(9)

This ratio illustrates cost-efficiency change only: values below one indicate improvement, values above one indicate deterioration, and one indicates no change.

3.2.3. Decomposition of Cost Productivity Change

To identify the sources of intertemporal cost productivity change, the CMPI is multiplicatively decomposed into five components:

$${\mathit{CMPI}}_k^{t,t+1}=\Delta {\mathit{PTE}}_k^{t,t+1}\times ∆T_k^{t,t+1} \times ∆{\mathit{AE}}_k^{t,t+1}\times ∆{\mathit{PE}}_k^{t,t+1}\times ∆{\mathit{CSE}}_k^{t,t+1}$$

(10)

The five components are multiplicatively linked to the aggregate CMPI, such that the decomposition provides an accounting identity for tracing observed cost-productivity changes to distinct efficiency, technological, price, and scale components.

Because each component is expressed under the same cost-efficiency-ratio orientation as the aggregate CMPI, the same interpretation rule applies:

$$\begin{array}{l}∆Z>1⟹\mathit{deterioration},\\ ∆Z<1⟹\mathit{improvement}\\ \hspace{1em}\hspace{1em} Zϵ\{\mathit{PTE},\mathit{T},\mathit{AE},\mathit{PE},\mathit{CSE}\}\end{array}$$

(11)

where the first component is the pure technical efficiency change (∆PTE), and the second component is the technological change (∆T), both defined as follows:

$$∆\mathit{PTE}={\displaystyle \frac{D_{\mathit{IV}}^{t+1}(y^{t+1},x^{t+1})}{D_{\mathit{IV}}^t(y^t,x^t)}}={\displaystyle \frac{{\mathit{TE}}_{\mathit{IV}}^t(y^t,x^t)}{{\mathit{TE}}_{\mathit{IV}}^t(y^{t+1},x^{t+1})}}$$

(12)

$$∆T={\left[{\displaystyle \frac{D_{\mathit{IV}}^t\left(y^{t+1},x^{t+1}\right)}{D_{\mathit{IV}}^{t+1}\left(y^{t+1},x^{t+1}\right)}}\times {\displaystyle \frac{D_{\mathit{IV}}^t\left(y^t,x^t\right)}{D_{\mathit{IV}}^{t+1}\left(y^t,x^t\right)}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(13)

The third component, Allocative efficiency change (∆AE), is the change in allocative efficiency defined as:

$$∆\mathit{AE}={\displaystyle \frac{C_{\mathit{IV}}^t(y^t,w^t)\times D_{\mathit{IV}}^t(y^t,w^t)/w^t{x}^t}{C_{\mathit{IV}}^{t+1}(y^{t+1},w^{t+1})\times D_{\mathit{IV}}^{t+1}(y^{t+1},w^{t+1})/w^{t+1}{x}^{t+1}}}$$

(14)

The subscript “V” in the cost function indicates that production costs are calculated under Variable Returns to Scale (VRS). The input-oriented allocative efficiency at period t, as proposed by Maniadakis and Thanassoulis (2004) [28], can be expressed as follows: $\mathit{AE}(y^t,x^t,w^t)=C_{\mathit{IV}}^t(y^t,w^t)\times D_{\mathit{IV}}^t(y^t,w^t)/w^t,x^t$. The Allocative Efficiency Change (∆AE) is used to measure the variation in allocative efficiency over time $∆:\mathrm{AE}={\mathit{AE}}_{\mathit{IV}}^t\left(y^t,x^t,w^t\right)/{\mathit{AE}}_{\mathit{IV}}^{t+1}\left(y^{t+1},x^{t+1},w^{t+1}\right)$. When the allocative efficiency $A{E}_t^V(y_t,x_t,w_t)=1$, it implies that R_CE = 1 is equal to technical efficiency.

The fourth component of the Cost Malmquist decomposition, Price effect change (∆PE), is the price effect change, i.e.,

$$∆\mathrm{PE}={\left[{\displaystyle \frac{\frac{C_V^{t+1}(y^t,w^{t+1})\times D_{\mathit{IV}}^{t+1}(y^t,x^t)}{w^{t+1}{x}^{t+1}}}{\frac{C_V^t(y^t,w^t)\times D_{\mathit{IV}}^t(y^t,x^t)}{w^t{x}^t}}}\times {\displaystyle \frac{\frac{C_V^{t+1}(y^{t+1},w^{t+1})\times D_{\mathit{IV}}^{t+1}(y^{t+1},x^{t+1})}{w^{t+1}{x}^{t+1}}}{\frac{C_V^t(y^{t+1},w^t)\times D_{\mathit{IV}}^t(y^{t+1},x^{t+1})}{w^t{x}^{t+1}}}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(15)

In Equation (15), the first term within the curly brackets on the right-hand side represents the change in the minimum-cost allocative efficiency of the base-period production (y_t,x_t) when the input prices w_t change to w_t+1. The second term denotes the change in the minimum-cost allocative efficiency for the current-period production (y_t+1,x_t+1). The Input Price effect change (∆PE) is defined as the geometric mean of these two ratios.

The fifth component of the Cost Malmquist Productivity Index (CMPI) is the Cost scale efficiency change (∆CSE), which is expressed as follows:

$$∆\mathit{CSE}={\left[{\displaystyle \frac{\frac{C_V^{t+1}(y^{t+1},w^{t+1})}{C_C^{t+1}(y^{t+1},w^{t+1})}}{\frac{C_V^{t+1}(y^t,w^{t+1})}{C_C^{t+1}(y^t,w^{t+1})}}}\times {\displaystyle \frac{\frac{C_V^{t+1}(y^{t+1},w^t)}{C_C^{t+1}(y^{t+1},w^t)}}{\frac{C_V^t(y^t,w^t)}{C_C^t(y^t,w^t)}}}\right]}^{{\displaystyle \frac{1}{2}}}$$

(16)

For example, in the ratio expression, ${\Delta \mathit{CSE}}_t(y_t,w_t)={\displaystyle \frac{C_V^t(y_t,w_t)}{C_C^t(y_t,w_t)}}$ indicates that, under the input prices w_t, the minimum-cost output level y_t corresponds to the optimal scale of production. Accordingly, the intertemporal Cost scale efficiency change (∆CSE) is given by: $\Delta \mathit{CSE}={({\displaystyle \frac{{\mathit{CSE}}_{t+1}(y_{t+1},w_{t+1})}{{\mathit{CSE}}_{t+1}(y_t,w_{t+1})}}\times {\displaystyle \frac{{\mathit{CSE}}_t(y_{t+1},w_t)}{{\mathit{CSE}}_t(y_t,w_t)}})}^{1/2}$which represents the geometric mean of the cost scale efficiencies for the specific output levels y_t and y_t+1 in periods t and t + 1.

3.2.4. DEA-Based Linear Programming Formulation

The following DEA-based linear programming problem for bank k:

$$k=\begin{array}{c}\mathit{min}\\ x,\lambda \end{array}{\omega }_k^{t^{\prime }}x$$

(17)

subject to

$$x\ge {\displaystyle {\sum }_{j=1}^N}{\lambda }_j{x}_j^t, y_k^t\le {\displaystyle {\sum }_{j=1}^N}{\lambda }_j{y}_j^t, {\displaystyle {\sum }_{j=1}^N}{\lambda }_j=1, {\lambda }_j\ge 0$$

(18)

Removing the convexity constraint yields the corresponding CRS formulation.

The measurement of the Cost Malmquist Productivity Index (CMPI), an input-oriented Malmquist productivity index, requires the estimation of cost functions $C_V^t(y_t,w_t)$ and $C_C^t(y_t,w_t)$ under Variable Returns to Scale (VRS) and Constant Returns to Scale (CRS), respectively.

For the kth decision-making unit (DMU), that is, the sample bank, the contemporaneous cost function $C_V^t\left(y_t,w_t\right)$ can be estimated using the following linear programming formulation:

$${}_{\mathrm{x},\mathsf{\lambda }}{}^{\mathrm{Min}}w_{\mathit{kn}}^t{x}_n=C_V^t\left(y^t,w^t\right)$$

(19)

$${\displaystyle {\sum }_{j=1}^J}{\lambda }_j{y}_{\mathit{jm}}^t\ge y_{\mathit{km}}^t, m=1,2,\dots ,M$$

(20)

$${\displaystyle {\sum }_{j=1}^J}{\lambda }_j{x}_{\mathrm{jn}}^{\mathit{t}}\le x_{\mathit{kn}}, n=1,2,\dots ,N$$

(21)

$${\displaystyle {\sum }_{j=1}^J}{\lambda }_j=1 {\lambda }_j\ge 0, x_n\ge 0$$

(22)

In Equation (22), by removing the constraint ${\sum }_{j=1}^J{\lambda }_j=1$, the contemporaneous cost function $C_C^t(y_t,w_t)$ under Constant Returns to Scale (CRS) can be obtained. Similarly, the intertemporal cost function $C_V^t(y_{t+1},w_{t+1})$ can be computed in the same manner as shown in the following equation:

$$\mathrm{Min} \mathrm{x}, \mathsf{\lambda }{w}_{\mathit{kn}}^t{x}_n=C_V^t\left(y^{t+1},w^t\right)$$

(23)

$${\displaystyle {\sum }_{j=1}^J}{\lambda }_j{y}_{\mathit{jm}}^t\ge y_{\mathit{km}}^{t+1}, m=1,2,\dots ,M$$

(24)

$${\displaystyle {\sum }_{j=1}^J}{\lambda }_j{x}_{\mathit{jn}}^t\le x_{\mathit{kn}}, n=1,2,\dots ,N$$

(25)

$${\displaystyle {\sum }_{j=1}^J}{\lambda }_j=1\hspace{1em}{\lambda }_j\ge 0,x_n\ge 0$$

(26)

Similarly, by removing the constraint ${\sum }_{j=1}^J{\lambda }_j=1$, other cost functions such as $C_V^{t+1}(y_{t+1},w_{t+1})$, $C_V^{t+1}(y_t,w_{t+1})$, $C_C^{t+1}(y_{t+1},w_{t+1})$, and $C_C^{t+1}\left(y_t,w_{t+1}\right)$ can likewise be calculated.

To measure technological change between t and t + 1, the cost functions are evaluated not only against the contemporaneous frontier but also against the intertemporal reference technology. The resulting cross-period cost functions provide the counterfactual cost measures required for the decomposition of the CMPI.

Using MATLAB, all DEA-based linear programming models and intertemporal cost functions were computed to obtain the overall CMPI and its five decomposed indices, namely Pure Technical Efficiency Change (ΔPTE), Technological Change (ΔT), Allocative Efficiency Change (ΔAE), Price Effect Change (ΔPE), and Cost Scale Efficiency Change (ΔCSE). These calculated indices served as the productivity measures for the subsequent panel regression analyses examining the effects of ESG performance on banking productivity. Illustrative numerical example. Under the deterioration-oriented convention, consider hypothetical component values of ΔPTE = 0.98, ΔT = 0.99, ΔAE = 0.97, ΔPE = 1.02, and ΔCSE = 1.01. Their product is 0.9695, which is below one and therefore indicates an overall improvement under this convention. The favorable movements in the first three components outweigh the unfavorable movements in the price and scale components. The reciprocal index is approximately 1.0314 and expresses the same outcome under an improvement-oriented convention. These hypothetical values illustrate multiplication and interpretation only; they are not empirical observations or a validation of the component formulas.

3.3. Panel Regression Models for ESG and Productivity

In the third stage, the previously calculated CMPI and its five components were used as dependent variables in separate pooled OLS regressions. EDS, SDS, and GDS were the explanatory variables, with LTA, NPR, and D01 included as controls. These models examine conditional associations rather than causal effects.

CMPI_i = β₀ + β₁ EDS_i + β₂ SDS_i + β₃ GDS_i + β₄ LTA_i + β₅ NPR_i + β₆ D01_i + ε_i

(27)

In this framework, the Cost Malmquist Productivity Index (CMPI) measures productivity changes across banks and over time, while ESG variables capture sustainability dimensions. Under variable returns to scale (VRS), CMPI is decomposed into five components: Pure Technical Efficiency Change (∆PTE), Technological Change (∆T), Allocative Efficiency Change (∆AE), Price Effect Change (∆PE), and Cost Scale Efficiency Change (∆CSE). Each component is regressed on Environmental (EDS), Social (SDS), and Governance (GDS) scores, controlling for bank size (LTA), non-performing loan ratio (NPR), and the study-specific period indicator (D01). This approach identifies the specific productivity channels associated with ESG performance, particularly environmental engagement, in Taiwan’s banking sector. The following equations specify the reported pooled OLS regressions. The pure technical efficiency change is as follows:

ΔPTE_i = β₀ + β₁ EDS_i + β₂ SDS_i + β₃ GDS_i + β₄ LTA_i + β₅ NPR_i + β₆ D01_i + ε_i

(28)

This equation assesses whether higher ESG performance is associated with better managerial and operational efficiency under existing technologies. The technological change is as follows:

ΔT_i = β₀ + β₁ EDS_i + β₂ SDS_i + β₃ GDS_i + β₄ LTA_i + β₅ NPR_i + β₆ D01_i + ε_i

(29)

This regression evaluates whether ESG practices are linked to the adoption or diffusion of innovations that shift the production frontier. The allocative efficiency change is as follows:

ΔAE_i = β₀ + β₁ EDS_i + β₂ SDS_i + β₃ GDS_i + β₄ LTA_i + β₅ NPR_i + β₆ D01_i + ε_i

(30)

This specification investigates whether banks with stronger ESG profiles better align input choices with efficiency objectives. The price effect is as follows:

ΔPE_i = β₀ + β₁ EDS_i + β₂ SDS_i + β₃ GDS_i + β₄ LTA_i + β₅ NPR_i + β₆ D01_i + ε_i

(31)

This model tests whether ESG engagement is associated with improved alignment to input-price conditions. The cost scale efficiency change is as follows:

ΔCSE_i = β₀ + β₁ EDS_i + β₂ SDS_i + β₃ GDS_i + β₄ LTA_i + β₅ NPR_i + β₆ D01_i + ε_i

(32)

This specification examines whether ESG performance is associated with changes in cost–scale efficiency over time. Together, Equations (28)–(32) translate the study’s overarching question concerning the relationship between ESG performance and bank productivity in Taiwan into component-level analyses of pure technical efficiency, technological change, allocative efficiency, price effects, and cost–scale efficiency. The pooled OLS estimates describe conditional associations and are not used to substantiate within-bank relationships or robustness claims. Accordingly, the results do not establish causal effects.

4. Research Results

This study follows the three-stage analytical framework described in the methodology section. First, ESG and financial data of Taiwan’s listed banks were collected and organized into a panel database. Second, MATLAB software was used to calculate the Cost Malmquist Productivity Index (CMPI) and its decomposed productivity indicators. Third, SPSS 22 regression procedures were employed to examine associations between ESG dimensions and productivity indicators. The research results are presented according to these three analytical stages.

4.1. Stage 1: Descriptive Statistics of ESG and Financial Data

In the first stage, ESG and financial data were obtained from the Taiwan Economic Journal (TEJ) database [27] and compiled into an Excel panel dataset covering 18 listed Taiwanese banks from 2017 to 2023. The variables included Environmental Dimension Score (EDS), Social Dimension Score (SDS), Governance Dimension Score (GDS), total assets (LTA), non-performing loan ratio (NPR), and the input–output variables required for CMPI estimation.

Table 2 presents the descriptive statistics and shows substantial heterogeneity across banks in organizational scale, resources, funding, and outputs. Average employment was 6226, ranging from 398 to 13,609 employees. Average outputs were 1,244,071,181, 195,431,082, and 10,025,562, with considerable cross-bank variation. Average employment increased from 5883 in 2017 to 6595 in 2023, while output volumes also increased, indicating sustained growth in banking activities.

Table 2. Taiwan’s Listed Bank Industries from 2017 to 2023 (Unit: NT$ thousands).

		X1	X2	X3	Y1	Y2	Y3	PX1	PX2	PX3
Full period	Mean	6226	17,694,452	1,743,888,956	1,244,071,181	195,431,082	10,025,562	1335	0.4885	0.0391
	Std. Dev.	2971	10,877,603	1,158,789,063	664,187,960	107,780,320	8,641,869	208	0.2830	0.1756
	Maximum	13,609	45,569,994	4,567,188,438	2,790,306,038	445,571,701	41,073,749	1917	1.3559	1.0019
	Minimum	398	2,387,498	95,867,762	142,947,865	28,197,495	1,487,395	796	0.0854	0.0022
2017	Mean	5883	17,079,506	1,567,792,960	1,037,178,475	150,363,692	8,945,044	1222	0.4621	0.0062
	Std. Dev.	2964	11,801,544	869,115,846	562,209,369	79,473,291	7,730,257	186	0.3242	0.0009
	Maximum	11,232	44,110,239	2,865,475,938	1,993,819,434	306,613,777	31,540,320	1647	1.3559	0.0085
	Minimum	398	2,392,392	224,477,116	142,947,865	31,192,871	1,487,395	880	0.0912	0.0050
2018	Mean	6005	17,537,793	1,326,094,576	1,088,717,533	155,511,765	9,072,835	1282	0.4785	0.0624
	Std. Dev.	2892	11,849,968	950,159,134	563,321,680	81,853,340	7,532,145	213	0.3107	0.2345
	Maximum	11,309	45,569,994	2,965,810,052	2,050,071,547	336,184,472	30,786,672	1694	1.2907	1.0019
	Minimum	954	2,387,498	96,770,449	152,229,752	28,197,495	1,627,650	796	0.1011	0.0055
2019	Mean	6160	17,443,096	1,403,611,426	1,122,686,997	183,457,671	9,986,078	1317	0.4901	0.1729
	Std. Dev.	2955	11,342,147	1,005,236,448	580,987,635	102,358,581	8,531,251	205	0.3002	0.3809
	Maximum	11,772	42,559,277	3,156,572,640	2,182,264,644	387,478,611	34,604,535	1708	1.2830	1.0010
	Minimum	975	2,706,831	104,211,169	155,350,678	30,947,973	1,695,428	876	0.1123	0.0057
2020	Mean	6262	17,599,249	1,528,338,943	1,178,507,460	208,133,073	9,809,864	1293	0.5068	0.0051
	Std. Dev.	3015	11,106,748	1,112,680,661	601,843,400	105,432,556	8,735,308	185	0.3153	0.0009
	Maximum	12,120	41,372,226	3,511,152,585	2,264,446,500	396,955,384	35,323,658	1683	1.3491	0.0069
	Minimum	960	2,966,680	105,672,908	184,901,230	40,088,916	1,903,514	907	0.1014	0.0036
2021	Mean	6287	17,577,351	1,665,703,061	1,258,379,985	219,172,624	10,427,204	1360	0.5190	0.0031
	Std. Dev.	3027	10,908,711	1,237,445,517	648,812,629	113,060,724	9,445,542	184	0.3211	0.0005
	Maximum	12,317	39,919,055	3,723,627,886	2,431,988,226	425,498,457	38,565,346	1731	1.3162	0.0041
	Minimum	971	2,957,881	95,867,762	206,356,935	46,442,931	2,051,193	931	0.0994	0.0022
2022	Mean	6374	18,156,320	2,291,989,319	1,448,230,419	222,000,071	10,163,373	1383	0.4741	0.0065
	Std. Dev.	3113	10,669,247	1,236,459,867	753,624,656	128,462,944	8,969,823	193	0.2155	0.0010
	Maximum	12,907	39,415,743	4,115,524,005	2,581,728,135	445,571,701	36,087,362	1737	0.8080	0.0085
	Minimum	1001	4,614,394	324,146,102	242,334,911	42,292,760	2,192,526	918	0.0902	0.0047
2023	Mean	6595	18,433,683	2,413,909,297	1,563,303,356	226,874,932	11,714,503	1480	0.4872	0.0154
	Std. Dev.	3274	10,267,149	1,297,910,471	820,679,977	121,562,788	10,373,474	213	0.2175	0.0028
	Maximum	13,609	39,411,605	4,567,188,438	2,790,306,038	444,193,029	41,073,749	1917	0.8451	0.0214
	Minimum	975	4,950,842	318,268,784	230,086,122	39,377,870	2,218,846	1128	0.0854	0.0102

Note: Data Source [29]: accessed on 30 May 2026 from https://tejpro.tej.com.tw/SchoolDoc/NCUE/?lang=zh-TW. This link iden-tifies the database access point; access to the underlying data requires institutional authorization.

Input prices varied over time. Average labor price rose from 1222 to 1480, while capital prices remained relatively stable at approximately 0.46–0.52. Funding prices showed greater volatility, particularly around 2019–2023. These variations provide essential input-price information for CMPI estimation and support the inclusion of bank-specific and time effects in subsequent analyses.

4.2. Stage 2: CMPI Measurement Results Using MATLAB

In the second stage, MATLAB software was employed to calculate the Cost Malmquist Productivity Index (CMPI) and its five decomposed components under the Variable Returns to Scale (VRS) framework. The computational procedure involved solving a series of DEA-based linear programming models and intertemporal cost functions for each bank and year. The resulting productivity indices provide a comprehensive assessment of productivity dynamics in Taiwan’s banking industry.

4.2.1. Overall CMPI Performance

Based on the input, output, and input-price variables collected from the TEJ database, a series of DEA-based linear programming models were solved to estimate intertemporal productivity changes for Taiwan’s listed banks from 2017 to 2023. Based on the cost-efficiency-ratio definition established in Section 3.2, CMPI > 1 indicates deterioration in cost productivity, CMPI < 1 indicates improvement, and CMPI = 1 indicates no change. The resulting CMPI values provide an overall assessment of productivity dynamics during the study period, as shown in Table 3.

Table 3. Cost Malmquist Productivity Index and Its Five-Way Decomposition for Taiwan’s Listed Banks, 2017–2023.

Year	CMPI	∆PTE	∆T	∆AE	∆PE	∆CSE
Base Year	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
2017–2018	1.1329	0.9431	1.0327	1.5375	0.7214	1.0486
2018–2019	1.0641	1.0198	0.9908	0.9837	0.9589	1.1165
2019–2020	1.1525	0.9933	1.0043	0.9107	1.3640	0.9300
2020–2021	0.9811	1.0128	0.9940	0.9427	1.0536	0.9812
2021–2022	1.0924	1.0361	0.9841	0.9223	1.1856	0.9799
2022–2023	0.9827	0.9807	1.0104	1.0302	0.9651	0.9975
Full period	1.0925	0.9980	1.0023	1.0467	1.0355	1.0077

Note: Under the cost-efficiency-ratio convention defined in Section 3.2, values greater than 1 indicate deterioration in cost productivity, values less than 1 indicate improvement, and values equal to 1 indicate no change. The CMPI satisfies the multiplicative decomposition CMPI = ΔPTE × ΔT × ΔAE × ΔPE × ΔCSE.

Table 3 reports the Cost Malmquist Productivity Index (CMPI) and its five components: ΔPTE, ΔT, ΔAE, ΔPE, and ΔCSE for 2017–2023. Values above 1 indicate productivity deterioration, while values below 1 indicate improvement. The reported full-period CMPI is 1.0925, which exceeds one. ΔAE (1.0467) and ΔPE (1.0355) are the main contributors, while ΔPTE (0.9980), ΔT (1.0023), and ΔCSE (1.0077) remain close to 1. These results suggest that allocative efficiency and input-price effects are the major sources of productivity variation, whereas managerial efficiency, technology, and scale effects remain relatively stable. The multiplicative decomposition was also verified for consistency across all consecutive-year observations.

4.2.2. Year-to-Year Productivity Changes

2017~2018: CMPI = 1.1329 (deterioration). The increase is driven primarily by ΔAE = 1.5375 and ΔCSE = 1.0486, partially offset by ΔPE = 0.7214 and ΔPTE = 0.9431. ΔT = 1.0327 is slightly above one.

2018~2019: CMPI = 1.0641 (deterioration). ΔCSE = 1.1165 and ΔPTE = 1.0198 push CMPI upward, while ΔT = 0.9908, ΔAE = 0.9837, and ΔPE = 0.9589 dampen the increase.

2019~2020: CMPI = 1.1525 (deterioration). ΔPE = 1.3640 is the dominant upward contributor. Offsetting movements include ΔAE = 0.9107 and ΔCSE = 0.9300, while ΔT = 1.0043 and ΔPTE = 0.9933 are near neutral.

2020~2021: CMPI = 0.9811 (improvement). Modest upward pressures from ΔPTE = 1.0128 and ΔPE = 1.0536 are more than offset by ΔAE = 0.9427. ΔT = 0.9940 and ΔCSE = 0.9812 remain close to one.

2021~2022: CMPI = 1.0924 (deterioration). ΔPE = 1.1856 and ΔPTE = 1.0361 lead the increase, while ΔAE = 0.9223, ΔT = 0.9841, and ΔCSE = 0.9799 mitigate it.

2022~2023: CMPI = 0.9827 (improvement). Reductions in ΔPE = 0.9651 and ΔPTE = 0.9807 pull CMPI below one, offsetting small increases in ΔT = 1.0104 and ΔAE = 1.0302. ΔCSE = 0.9975 is effectively neutral.

Table 3 reveals two main patterns. First, ΔAE and ΔPE account for most CMPI values above 1, indicating that allocative decisions and input-price changes are the main sources of productivity variation. Second, ΔPTE, ΔT, and ΔCSE generally remain close to 1, suggesting relative stability in managerial efficiency, technological change, and scale effects. Taiwanese banks therefore appear more sensitive to input-price fluctuations than technological progress. Year-to-year results also show substantial external effects, with the strongest deterioration in 2019–2020 and improvements in 2020–2021 and 2022–2023.

4.3. Preliminary Pooled OLS Results

Table 4 presents preliminary pooled OLS results examining the relationship between ESG dimensions and cost productivity. CMPI and its five components are modeled separately, with EDS, SDS, and GDS as key explanatory variables and LTA, NPR, and D01 as controls. The results indicate that environmental performance is more strongly associated with cost productivity than social or governance performance. In the CMPI model, EDS is negative and significant, while SDS and GDS are insignificant. Since a lower CMPI indicates improved cost productivity, the negative EDS coefficient suggests that stronger environmental performance is associated with productivity improvement.

Table 4. Preliminary Pooled OLS Results for Cost Malmquist Productivity.

Variable	Coefficient	Std. Error	t-Value	Prob.
EDS(Environmental Dimension Score)	−0.0065	0.0023	−2.84	0.0053
SDS(Social Dimension Score)	−0.0039	0.0025	−1.55	0.1248
GDS(Governance Dimension Score)	−0.0016	0.0038	−0.43	0.6655
LTA(Log of Total Assets)	0.0032	0.0410	0.08	0.9389
NPR(Non-Performing Loan Ratio)	−0.7811	0.3711	−2.11	0.0374
D01 (Study-Specific Period Indicator)	0.2607	0.0589	4.42	0.0000
C (Constant)	1.5974	0.9823	1.63	0.1066
Statistic	Value	Statistic		Value
R2	0.24	Mean dependent var		0.85
Adjusted R2	0.21	S.D. dependent var		0.36
S.E. of regression	0.32	Akaike info criterion		0.64
Sum squared resid.	12.47	Schwarz criterion		0.79
Log likelihood	−33.04	Hannan–Quinn criterion.		0.70
F-statistic	6.41	Durbin–Watson stat		0.61
Prob. (F-statistic)	<0.001

Note: Dependent Variable: CMPI/Method: OLS/Sample: 1–108/Included Observations: 108. Unit: bank-transition observations.

Although the pooled OLS results provide useful preliminary evidence, the relatively low Durbin–Watson statistic indicates potential serial correlation in the residuals. Moreover, pooled OLS does not control for time-invariant bank-specific characteristics that may influence both ESG performance and productivity. The pooled OLS results are retained as exploratory evidence. Their reported significance levels have not been demonstrated to be robust to within-bank residual dependence.

4.3.1. Regression Results for Overall CMPI

(1)

Effects of ESG Dimensions on Overall CMPI

Table 4 reports pooled OLS results with CMPI as the dependent variable. Since lower CMPI indicates improved cost productivity, negative coefficients imply productivity improvement. EDS is negative and significant (−0.0065, p = 0.0053), indicating that stronger environmental performance is associated with improved cost productivity. In contrast, SDS (−0.0039, p = 0.1248) and GDS (−0.0016, p = 0.6655) are insignificant. Thus, environmental performance is the most significant ESG dimension associated with CMPI.

(2)

Effects of Control Variables

NPR is negative and significant (−0.7811, p = 0.0374), indicating lower CMPI as credit risk increases, although this counterintuitive result requires robustness checks. LTA is insignificant (0.0032, p = 0.9389), suggesting no clear size effect. D01 has a positive coefficient (0.2607, p < 0.001 under the reported inference procedure), indicating higher CMPI values for observations coded as one, conditional on the included controls. The negative association between NPR and CMPI is counterintuitive, and its underlying explanation remains unverified. Future research could examine lagged NPR, alternative asset-quality measures, and bank-level restructuring information. The present result should not be interpreted as evidence that deteriorating asset quality improves productivity.

(3)

Model Diagnostics and Summary of Overall CMPI Results

The regression explains approximately 24.4% of the variation in CMPI (R² = 0.244; adjusted R² = 0.206) and is statistically significant (F = 6.407, p < 0.001). However, the low Durbin–Watson statistic (0.61) indicates residual serial correlation, requiring robustness checks using clustered standard errors and fixed-effects models. The results show that EDS is the only ESG dimension significantly associated with CMPI. Its negative coefficient indicates that stronger environmental performance is associated with improved cost productivity among Taiwan’s listed banks during 2017–2023. In contrast, SDS and GDS are statistically insignificant. The study-specific period indicator (D01) is positive and significant, while the NPR result requires further investigation. Overall, environmental performance emerges as the primary ESG dimension associated with aggregate banking productivity.

4.3.2. Regression Results for CMPI Components

Table 5 reports the pooled OLS associations between ESG dimensions and the five CMPI components, conditional on the included controls. Environmental performance has negative coefficients for ΔPTE, ΔT, and ΔAE that are statistically significant under the reported inference procedure, whereas the coefficients for ΔPE and ΔCSE are statistically insignificant. These findings are interpreted as preliminary conditional associations because residual-dependence and finite-sample inference concerns remain unresolved. They do not establish that environmental engagement causes productivity improvement or operates through empirically verified sustainability mechanisms.

Table 5. Environmental Performance and Decomposed Cost-Productivity Components.

Variable	ΔPTE	ΔT	ΔAE	ΔPE	ΔCSE
EDS	−0.0059 *** (0.0022)	−0.0067 *** (0.0022)	−0.0098 ** (0.0041)	−0.0047 (0.0033)	−0.0123 (0.0077)
SDS	−0.0040 * (0.0024)	−0.0041 * (0.0024)	−0.0035 (0.0045)	−0.0042 (0.0037)	0.0018 (0.0037)
GDS	−0.0026 (0.0036)	−0.0016 (0.0036)	−0.0014 (0.0068)	−0.0013 (0.0056)	−0.0034 (0.0054)
LTA	0.0236 (0.0387)	0.0188 (0.0392)	−0.0619 (0.0736)	0.0111 (0.0600)	0.0307 (0.0458)
NPR	−0.7257 ** (0.3506)	−0.6600 * (0.3552)	−0.4707 (0.6671)	−0.9841 * (0.5436)	−0.8479 ** (0.4145)
D01	0.3039 *** (0.0557)	0.2753 *** (0.0564)	0.1165 (0.1060)	0.4385 *** (0.0864)	0.2887 *** (0.0658)
Constant	1.1679 (0.9282)	1.2719 (0.9403)	3.2265 * (1.7661)	1.3088 (1.4390)	1.0996 (1.0972)
N	108	108	108	108	108
R2	0.30	0.27	0.08	0.22	0.22
Adj. R2	0.26	0.2362	0.03	0.18	0.19
S.E. of reg.	0.31	0.31	0.58	0.47	0.36
F-statistic (p-value)	8.29 (0.000)	7.30 (0.000)	1.60 (0.153)	5.57 (0.000)	5.73 (0.000)
Durbin–Watson	0.49	0.49	1.15	1.30	0.86

Note: 1. Dependent variables are the CMPI components: ΔPTE (pure technical efficiency change), ΔT (Technological Change), ΔAE (allocative efficiency change), ΔPE (price effect), and ΔCSE (cost scale efficiency change). Estimator: pooled OLS. Standard errors in parentheses. 2. Statistical significance: * p < 0.10, ** p < 0.05, *** p < 0.01. By construction, component values greater than 1 indicate deterioration relative to the previous period, and values less than 1 indicate improvement. A negative coefficient is therefore associated with a reduction in the component and, under this convention, an improvement. Unit: bank-transition observations.

(1)

Associations of ESG Dimensions on CMPI Components

This subsection examines the association between ESG dimensions and the five CMPI components using the pooled OLS estimates in Table 5. Interpretation follows the study’s convention that component values above one reflect deterioration and values below one reflect improvement. Hence, a negative coefficient indicates an association with improvement in the corresponding channel.

The environmental score is negative and statistically significant for ΔPTE (p = 0.007) and ΔT (p = 0.003), and also negative and significant for ΔAE (p = 0.019). These results indicate that stronger environmental performance is associated with improvements in technical and allocative efficiency. The estimates for ΔPE and ΔCSE are negative but not statistically significant, suggesting limited direct association with price alignment or scale efficiency in the baseline pooled OLS specification.

Social scores are negative and marginally significant for ΔPTE (p = 0.092) and ΔT (p = 0.091), while governance scores are negative but statistically indistinguishable from zero across all components. Collectively, these patterns suggest that, conditional on controls, the environmental pillar is the principal ESG dimension associated with component-level improvements, with the social pillar displaying weaker and less precisely estimated associations, and the governance pillar showing no detectable effects in the baseline.

(2)

Associations of Control Variables

The non-performing loan ratio (NPR) is negative and significant for ΔPTE (p = 0.04) and ΔCSE (p = 0.043), and negative at the 10 percent level for ΔT (p = 0.07) and ΔPE (p = 0.073). Under the adopted index convention, the negative NPR coefficients correspond to lower component values, but they do not establish that deteriorating asset quality improves productivity. Bank size (LTA) is not statistically significant in any component, indicating no systematic association with component movements in the pooled OLS setting. The study-specific period indicator (D01) is positive and highly significant for ΔPTE, ΔT, ΔPE, and ΔCSE, and insignificant for ΔAE. The positive D01 coefficients indicate higher component values for observations coded one, conditional on the included controls. Their interpretation remains limited by the unresolved temporal definition of D01 and should not be treated as evidence of p.

(3)

Model Diagnostics and Goodness-of-Fit

Model fit is moderate and comparable across components. R² ranges from 0.08 (ΔAE) to 0.30 (ΔPTE). F-tests indicate joint significance for ΔPTE, ΔT, ΔPE, and ΔCSE, while the ΔAE regression is not jointly significant at conventional levels. Durbin–Watson statistics for ΔPTE, ΔT, and ΔCSE are below one, which points to serial correlation in pooled OLS residuals. The low Durbin–Watson statistics raise concerns about residual serial dependence. Fixed effects alone do not correct standard errors for such dependence. Because inference adjusted for within-bank correlation and the limited number of bank clusters has not been demonstrated, the reported component-level significance should be interpreted as preliminary rather than robust evidence.

(4)

Summary of Component-Level Results

The pooled OLS component regressions report negative environmental-performance coefficients for ΔPTE, ΔT, and ΔAE that are statistically significant under the reported inference procedure. The corresponding estimates for ΔPE and ΔCSE are statistically insignificant. These findings describe component-specific conditional associations rather than verified mechanisms through which environmental engagement improves productivity. The NPR and D01 coefficients require cautious interpretation because their underlying explanations remain unverified. Overall, the component regressions complement the aggregate CMPI analysis by distinguishing associations across productivity dimensions, subject to unresolved residual-dependence and finite-sample inference concerns.

4.4. Discussion and Analysis

The main findings of this study are as follows:

(1)

Pooled OLS Results for CMPI Components

The pooled component regressions describe associations with separate dimensions of cost-productivity change. Environmental performance is significantly associated with pure technical efficiency change, technological change, and allocative efficiency change. In contrast, the associations with changes in price effect and cost scale efficiency are statistically insignificant. This finding suggests that environmental performance is associated with technological change rather than merely static operational efficiency.

(2)

Environmental Performance and Specific Cost-Productivity Channels

The reported pooled OLS estimates show negative coefficients for environmental performance in the CMPI, ΔPTE, ΔT, and ΔAE models, consistent with the proposed directional hypotheses. However, their statistical significance remains subject to unresolved residual-dependence and finite-sample inference concerns. These findings are therefore treated as preliminary conditional associations rather than robust hypothesis confirmation or evidence of causal mechanisms. The statistically insignificant ΔPE and ΔCSE estimates likewise do not establish the absence of relationships.

The descriptive decomposition and the ESG regressions address different questions. The decomposition summarizes movements in CMPI and its constituent indices, with allocative efficiency and price effects showing prominent movements over the study period. It does not attribute these movements to environmental performance. By contrast, the pooled OLS regressions examine associations between environmental performance and each component, conditional on the included controls. Environmental performance is significantly associated with ΔPTE, ΔT, and ΔAE in the reported models, whereas the ΔPE and ΔCSE estimates are statistically insignificant. These patterns are not contradictory: a component may account for substantial productivity variation without being significantly associated with environmental performance. Accordingly, the results describe component-specific conditional associations rather than demonstrated mechanisms through which environmental engagement changes productivity.

5. Conclusions, Limitations, and Future Works

5.1. Conclusions

This study provides a decomposed description of bank cost-productivity change and exploratory evidence concerning its association with environmental performance. The reported pooled estimates suggest associations with selected productivity components, but unresolved inference and identification limitations prevent robust statistical or causal conclusions. The findings motivate policy options for further evaluation rather than establish their effectiveness.

(1)

The technological change association provides a rationale for considering targeted support for environmental data-processing and risk management technologies, such as AI-assisted climate risk assessment and digital carbon-accounting platforms. Subject to applicable policy frameworks, tax incentives or investment subsidies could be evaluated through pilot programs with clearly defined measures of implementation costs, processing efficiency, and environmental data quality. These are potential applications of the findings, not interventions whose effectiveness this study has established.

(2)

The theoretical framework and exploratory associations motivate evaluation of whether integrating environmental information into credit assessment and reviewing analytical resource allocation can improve banking operations. Regulators could support these efforts through standardized environmental data guidance and staff-training initiatives.

(3)

Environmental initiatives merit further evaluation, but the present estimates do not establish their priority over social or governance initiatives. However, the statistically insignificant social and governance coefficients do not justify reducing attention to these dimensions, whose benefits may concern employee welfare, accountability, risk resilience, or longer-term outcomes beyond the measures examined here. Overall, the findings inform the design and evaluation of environmental initiatives but do not establish the causal effectiveness of subsidies, tax incentives, or ESG policy priorities.

The conceptual contribution is to distinguish three potential organizational responses to environmental information requirements: improving processes under existing technology, upgrading technological capability, and adjusting input combinations relative to their costs. Mapping these responses to ΔPTE, ΔT, and ΔAE provides a theoretical interpretation of component-specific associations beyond the integration of ESG indicators with productivity measurement. The reported findings are consistent with this framework but do not directly measure environmental practices or establish causal transmission mechanisms.

5.2. Limitations and Future Works

This study has six limitations that suggest directions for future research.

(1)

Sample scope and size. The analysis covers 18 listed Taiwanese banks and 108 bank-transition observations. Its geographic concentration limits generalizability across regulatory environments, while repeated observations within banks should not be regarded as independent. The small sample constrains precision and statistical power. A theory-guided specification and consistency across reported models do not eliminate finite-sample concerns. Future research could include additional banks, countries, and observation periods.

(2)

ESG measurement. ESG indicators based on public reports may not fully capture qualitative aspects of sustainability performance or the implementation of environmental practices. Similar scores may reflect different combinations of activities and disclosure. Future studies could incorporate practice-specific indicators and qualitative evidence to improve measurement and interpretation.

(3)

Serial dependence and inference. Residual serial dependence may affect the precision of the reported estimates. Bank and year fixed effects account for persistent heterogeneity and common temporal shocks but do not themselves establish inference robust to serial correlation. With only 18 bank clusters, appropriate clustered inference requires explicit reporting and finite-sample consideration. The reported significance levels, particularly in the pooled component regressions, therefore warrant caution. Insignificant estimates should not be interpreted as evidence that relationships are absent.

(4)

Endogeneity. Reverse causality and omitted time-varying confounding remain possible. More productive banks may have greater resources for environmental activities, and changing managerial strategies may influence both environmental scores and productivity. The findings therefore represent conditional associations rather than causal effects. Future research could examine lagged environmental performance and alternative specifications, although lagging alone would not establish exogeneity.

(5)

Variable construction. Documentation of ESG scores, inputs, outputs, and input prices requires greater detail. Future research should report source fields, calculation formulas, units, and economic interpretation to improve reproducibility. Input prices deserve particular attention because their construction is central to cost-frontier estimation and the interpretation of allocative efficiency and price effects.

(6)

Period-indicator interpretation. D01 should be interpreted as a study-specific period indicator rather than a precise measure of pandemic exposure. Its designation as “2019–2021” does not imply that the pandemic began in 2019. Future research should explicitly clarify its temporal alignment with bank-transition observations and compare alternative period definitions to assess sensitivity to the selected observation window.