Incorporating Carbon Fees into the Efficiency Evaluation of Taiwan’s Steel Industry Using Data Envelopment Analysis with Negative Data ^†

Abstract

Carbon fees are scheduled to be levied in Taiwan, posing unprecedented challenges for the steel industry, given its high emissions and risk of carbon leakage. This study explores the potential impact of this policy on steel industry performance by incorporating projected carbon fees into the efficiency assessment. The Slacks-Based Measure (SBM) and Super SBM models in Data Envelopment Analysis (DEA), which account for negative data, are used to evaluate the operational efficiencies of 30 listed steel firms across supply chain segments in 2024 under baseline and carbon fee scenarios. Results reveal that incorporating the carbon fees mitigates the upward bias that overestimates inefficient firms’ SBM scores, triggers broad efficiency declines and ranking reshuffling (most severe upstream, moderate midstream, and least downstream), and widens cross-firm efficiency dispersion. Moreover, the study finds that excessive carbon fees and operating profit deficiencies are the main input- and output-side drivers of inefficiency, highlighting improvement potential in carbon cost management and profitability gains. To date, the efficiency implications of carbon fees for Taiwan’s steel industry have remained underexplored. Our findings offer empirical insights and a timely reference for steel firms to refine sustainability strategies ahead of forthcoming carbon fees.

1. Introduction

Deficient control of greenhouse gas emissions is heightening global warming, driving more severe climate change, and causing more hazardous extreme weather worldwide. These phenomena have caused widespread disruptions to ecosystems and food production while posing threats to human survival [1]. The scientific community has long warned that climate change may reach an irreversible level without effective actions [2]. In response, the net-zero emissions goal has become a global consensus, motivating nations to implement measures aimed at mitigating the environmental impacts of carbon emissions [3]. Among these measures, carbon pricing has emerged as a critical economic tool to facilitate carbon reductions. Its fundamental principle is to internalize the external costs of carbon emissions using market mechanisms, thereby incentivizing businesses and individuals to lower their carbon footprints [4]. Grounded in the Polluter Pays Principle, carbon pricing assigns a per-ton price to carbon dioxide equivalent (CO2e) emissions, such that heavier emitters bear higher compliance costs [5]. Carbon pricing commonly centers on two instruments, including carbon taxes and emissions trading systems (ETSs) [6]. A carbon tax directly levies a fee on each unit of carbon emitted, increasing the financial burden of continued high emissions and thereby fostering the adoption of cleaner technologies. In contrast, an ETS puts a cap on total emissions and permits firms to trade emission allowances, offering flexibility with an allowance price discovered in the market [7]. According to the World Bank [8], 75 carbon pricing instruments (39 carbon taxes and 36 ETSs) have been implemented globally, covering approximately 24% of global emissions.

Taiwan’s Climate Change Response Act, which entered into force in February 2023, establishes the legal foundation for implementing carbon fees as a carbon pricing mechanism that employs economic incentives to facilitate corporate carbon reduction initiatives [9,10,11]. On 1 January 2025, Taiwan officially implemented a carbon fee policy targeting high-emission firms [12]. The first carbon fee will be levied and collected in May 2026, calculated according to each firm’s emissions from the entire year of 2025 [13]. All revenue from carbon fees is planned to be directed into the “Greenhouse Gas Management Fund” [14]. This fund is specifically designed to finance greenhouse gas reduction efforts, the development of low-carbon and negative-emission technologies, and industry advancement [11,14]. As a cornerstone of industrial economies, the steel industry not only significantly contributes to national economic growth and development but is also closely tied to building stock, with the construction sector being a major consumer and key driver of steel demand [15]. However, the steel industry is capital-intensive and operationally inflexible, and its heavy dependence on fossil fuels causes substantial carbon emissions that exacerbate global climate change [16]. This environmental impact has placed the steel sector under intense scrutiny from policymakers and other stakeholders, particularly amid the rollout of carbon pricing mechanisms. Consequently, effective carbon emission management in the steel industry has become increasingly important, not only during the production process but also throughout the entire life cycle of steel products, as emphasized in [17]. The carbon fee in Taiwan is expected to pose significant challenges to the steel industry, still in post-COVID-19 recovery, as heavy carbon-related cost burdens may lead to financial losses and weaken the global competitiveness of domestic steel firms.

Data Envelopment Analysis (DEA), proposed by Charnes, Cooper, and Rhodes [18], evaluates the efficiency of Decision-Making Units (DMUs) by examining how they convert input variables into output variables. It has been widely used as a primary method for performance benchmarking and carbon emissions mitigation in sustainability literature, particularly in energy-intensive industries. For example, Takayabu et al. [19] used DEA in the global metal industry to assess productive efficiency and then estimated Scopes 1–3 carbon reduction potentials under GHG Protocol standards. Their findings show that the basic iron and steel sector is the largest metal-sector emitter and exhibits a reduction potential of 354.4 Mt, of which 71% arises from Scope 1 emissions. Wu et al. [20] employed a zero-sum gains DEA (ZSG-DEA) model to optimize the allocation of carbon quotas among six energy-intensive industries in China, using quotas projected under IPCC 2 °C and 1.5 °C scenarios. The iron and steel industry revealed notably low allocation efficiency and had one of the greatest potentials for emissions reduction, with required cuts exceeding 40 Gt of carbon emissions in both scenarios. Recently, Wu et al. [21] applied the DEA to build a total-factor carbon efficiency index (TCPI) for China’s provinces and used the Synthetic Control Method (SCM) to derive a synthetic group to assess changes in TCPI before and after Carbon Emission Trading Scheme (CETS) implementation. The study found that the CETS significantly increased carbon emission efficiency in pilot provinces, with the policy effect strengthening over time. Despite these advances, research incorporating carbon fees into DEA-based efficiency assessments remains relatively limited, and evidence of its impact on operational efficiency in Taiwan’s steel industry is still absent. Addressing this gap, Lin et al. [9] used DEA with undesirable output (carbon emissions) to make an initial attempt at comparing the efficiency of the steel industry under both carbon fee and carbon emission scenarios. However, their study did not include a traditional baseline scenario (without carbon fees or carbon emissions), which would have enabled a more concrete assessment of the specific impact of carbon fee implementation on operational efficiency. Moreover, the carbon fee rate adopted in their analysis was a subjective assumption that may not reflect current practical conditions and limits the applicability of their findings.

This study employs both the Slacks-Based Measure (SBM) and Super SBM models in DEA, which are capable of handling negative values, to assess the operational efficiency of firms in the upstream, midstream, and downstream segments of the steel industry supply chain under two distinct scenarios, with one considering carbon fees and the other without considering carbon fees. The carbon fee incorporated into the efficiency assessment was simulated based on the latest rate announced by the Ministry of Environment and the actual emission data. Specifically, this research pursues three primary objectives. First, it investigates the operational efficiency of steel firms under the traditional scenario (without carbon fees) and the scenario with carbon fees. Second, it conducts a comparative analysis of efficiency and ranking changes among different segments of the steel supply chain. Third, it explores the potential for efficiency improvement among less efficient firms as well as the competitive advantages of efficient firms under the carbon fee scenario.

The remainder of the study is outlined below. Section 2 reviews the relevant literature on efficiency assessment in the steel industry. Section 3 presents the SBM and Super SBM models used in this study. Section 4 details the steel-firm sample and data collection. Section 5 reports the empirical results along with discussion. Finally, we conclude the study and highlight avenues for future research in Section 6.

2. Literature Review

Over the last few decades, a considerable number of studies have adopted DEA models to assess the efficiency of the steel industry. Ray and Kim [22] conducted a cost efficiency analysis in the U.S. steel industry using DEA. Their study aimed to evaluate potential cost savings by addressing technical and allocative inefficiencies within production technologies. They highlighted that improving both technical and allocative efficiency is crucial for enhancing the competitiveness of the industry. Ma et al. [23] used DEA and the Malmquist productivity index to investigate technical efficiency and its changes among 88 Chinese iron and steel firms and discussed factors influencing efficiency and productivity. Results revealed that centrally supervised firms exhibited superior technical efficiency but limited productivity growth. Additionally, medium-sized firms achieved notable improvements in scale efficiency and ongoing productivity gains. Firms with a diversified product structure showed the strongest productivity growth, mainly driven by technical efficiency progress. Yang and Choi [24] conducted an efficiency assessment of five global steel firms using CCR, BCC, and SBM models. Their findings indicate that the asset-oriented framework offers greater discriminant power among firms. Within this framework, Hitachi Metals Ltd. from Japan and Doosan Heavy Industries from Korea outperformed the others. Improvement directions for the inefficient firms are tighter cash and inventory management, coupled with long-term optimization of property, plant, and equipment. Debnath and Sebastian [25] used output-oriented DEA to assess the technical and scale efficiencies of 22 Indian steel firms. The analysis shows that some public sector firms were technically efficient but scale-inefficient due to unfavorable operations, while certain private firms excelled in both aspects, highlighting the need for technological modernization and better resource allocation to close the productivity gap with global competitors. Drawing on panel data for 26 provinces over 1996–2010, Yang et al. [26] applied a bootstrap network DEA approach to examine the technical efficiency of the iron and steel industry at the provincial level in China. The results indicate significant geographic disparities, with eastern and coastal economic zones outperforming central and western areas.

Beyond these applications, the literature also encompasses environmental and sustainability concerns. Some studies are concerned with energy efficiency. Applying DEA and the Malmquist Index, which accounts for undesirable outputs, He et al. [27] assessed energy efficiency and productivity growth of 50 Chinese iron and steel firms during 2001 to 2008. Low average energy efficiency in the steel industry was found, largely attributable to the inefficiency and technological lag of small and medium-sized firms. Also, the research emphasized that neglecting undesirable outputs leads to a biased estimate of efficiency and technical changes, and that environmental regulations could incentivize technological innovation and efficiency improvements. Ohlan [28] applied DEA to India’s firm-level data from 2004 to 2012 to assess energy efficiency in the iron and steel industry. The findings suggest that larger firms and those with higher labor productivity achieved better energy efficiency, while small and medium-sized firms retain considerable potential for improvement, thereby requiring further energy-saving efforts. Kim et al. [29] integrated a common-weights DEA window approach with the Malmquist productivity index and applied it to 45 Chinese iron and steel firms over the period 2009–2017 to evaluate energy and environmental efficiency. The results indicate that larger firms generally demonstrated greater energy efficiency, while smaller firms excelled in environmental efficiency. Kim et al. [30] presented a stepwise benchmarking DEA method with Dijkstra’s algorithm to measure the energy efficiencies of 42 Chinese steel firms. This approach offers inefficient firms the shortest learning paths, facilitating gradual improvements toward best practices in energy management.

Other studies focus on sustainable manufacturing performance. Wu et al. [31] proposed a modified two-stage network DEA model to measure the efficiencies of main manufacturing (Stage 1) and wastewater recycling and treatment (Stage 2) processes among 30 Chinese steel firms. They showed that most firms cannot reach full efficiency, and that system inefficiency was primarily attributed to the main manufacturing process. Gong et al. [32] integrated the Evidential Reasoning (ER) approach with the cross-efficiency DEA method to assess the clean production performance of four steel firms, using ten performance indicators drawn from quality and financial dimensions. By incorporating both self- and peer-evaluations, the study captured the competition among firms and provided a more objective ranking of clean production performance. Based on a sample of 54 Chinese iron and steel firms, Wang et al. [33] evaluated process efficiencies of sintering, coking, ironmaking, steelmaking, and steel rolling, applying DEA models. The findings revealed that SBM and Bootstrap-DEA yielded lower, more dispersed efficiency results. Regional disparities are evident, with southern firms excelling in certain processes but lagging overall. Using the total-factor perspective, Li et al. [34] employed a four-stage SBM model to examine the waste gas treatment efficiency of 65 Chinese iron and steel firms during 2005 to 2014. By decomposing total treatment efficiency into managerial and environmental components, the study found a general upward trend in total treatment efficiency and environmental efficiency, while managerial efficiency exhibited a slight decline, suggesting that treatment improvements were positively driven by external environmental factors rather than internal management factors. To address overcapacity, Fukuyama et al. [35] proposed a DEA model featuring an unrestricted capacity directional output distance function to assess capacity utilization among 48 major Chinese iron and steel firms from 2009 to 2013. By jointly considering emission-causing and non-emission-causing inputs as well as desirable and undesirable outputs, the study identified several types of excess capacity within firms. Later, Fukuyama et al. [36] advanced the work of Fukuyama et al. [35] by explicitly allowing for the adjustment of quasi-fixed inputs and employing joint weak disposability to better reflect intermediate-run realities in the capacity utilization analysis. Using a process-level DEA with the SBM, Li et al. [37] assessed green technical efficiency in 31 Chinese iron and steel enterprises by decomposing operations into sintering, ironmaking, and steelmaking processes. The steelmaking process underperformed the others and was the main constraint on system-wide efficiency improvement, and environmental regulation impacts were found to vary by process.

There is also a body of literature on environmental performance and on broader sustainability performance. Choi et al. [38] used the SBM model to evaluate the sustainable performance of 20 Korean steel firms covered in ETS from 2011 to 2015. The study evidenced that including greenhouse gas emissions as an undesirable output in the assessment helps avoid the bias of overestimation. The findings also suggest that upgrading operational scale with green investments could improve efficiency for most steel firms. Li et al. [39] employed a slacks-based global DEA with bootstrap correction to examine the environmental governance efficiency (EGE) of 86 Chinese iron and steel firms, and adopted a global Malmquist index to capture EGE changes over the period from 2005 to 2014. The study also explored the impact of market incentive environmental regulation (MIER) and command-and-control environmental regulation (CCER) on EGE using the econometric model, and found that MIER exhibited an inverted U-shaped impact on EGE, while CCER showed a positive but not significant association with EGE. Liu et al. [40] applied the Super SBM model that incorporates undesirable outputs to panel data on 54 Chinese iron and steel firms over 2009–2017 to evaluate their environmental performance. The study identified an inverted U-shaped link between environmental performance and return on assets (ROA), highlighting the strategic need to balance environmental and economic goals for sustainable growth. Applying a range-adjusted measure (RAM) within the DEA framework, Ding et al. [41] evaluated firm-level environmental protection performance in both the static and dynamic perspectives. The global Malmquist productivity index (GM index) was adopted to trace changes in both efficiency and technological progress of 49 Chinese iron and steel firms from 2015 to 2017. The findings reveal that most firms maintained high environmental efficiency, and growth in productivity was limited and varied across regions.

3. Methods

Data Envelopment Analysis (DEA) is an optimization-driven, non-parametric approach for benchmarking efficiency and analyzing productivity. The early CCR and BCC DEA models are based on radial measure, which assumes uniform proportional changes across all inputs and outputs [42,43]. However, this assumption overlooks inefficiencies stemming from slack variables in inputs and outputs. To remedy this, Tone [44] introduced the non-radial SBM (Slacks-Based Measure) model, which directly incorporates them. As a result, the SBM model provides a more rigorous and realistic assessment of efficiency, effectively preventing the overestimation that may occur with traditional radial models [45]. The SBM model is as follows [44]:

$$\mathrm{m}\mathrm{i}\mathrm{n} {\theta }_{0 }={\displaystyle \frac{1-\frac{1}{m}\sum _{i=1}^m\frac{s_i^{-}}{x_{io}}}{1+\frac{1}{s} \sum _{r=1}^s\frac{s_r^{+}}{y_{ro}^g}}}$$

$$\mathrm{s}.\mathrm{t}. {\sum }_{j=1}^n{\lambda }_j{x}_{ij}=x_{io}-s_i^{-} i=1,\dots ,m$$

$${\sum }_{j=1}^n{\lambda }_j{y}_{rj}^g=y_{ro}^g+s_r^{+} r=1,\dots ,s$$

(1)

$${\lambda }_j\ge 0,s_i^{-}\ge 0,s_r^{+}\ge 0$$

In this model (1), there exist n DMUs, i.e., steel firms, that feature m inputs and s desirable outputs. The ith input used by the jth DMU is symbolized by $x_{ij}$, while the rth desirable output produced by jth DMU is expressed as $y_{rj}^g$. Furthermore, $s_i^{-}$ is the slack variable capturing the excess of input i, and $s_r^{+}$ is the slack variable capturing the shortfall of desirable output r. Note that ${\theta }_0$ is restricted to the interval from 0 to 1, indicating the relative efficiency of the DMU, specifically the steel firm under assessment.

A significant limitation of the SBM model is its inability to accommodate negative data, which frequently arise in diverse real-world contexts. For instance, in finance, negative returns and net losses are commonly observed. Beyond finance, negative values are also common in areas such as environmental management (e.g., net emissions reductions) and healthcare (e.g., negative growth rates in patient outcomes). In order to transform negative data into positive values, this study utilizes the Base-Point Transformation method as proposed by Tone et al. [46], whereby all input and output variables are individually shifted by subtracting their respective base points. Specifically, variables containing negative values are converted to positive values by applying the transformations ${\overline{x}}_{ij}=x_{ij}-x_i^{min} (i=1,\dots ,m;j=1,\dots n)$ for inputs, and ${\overline{y}}_{rj}^g=y_{rj}^g-y_r^{min g}(r=1,\dots ,s;j=1,\dots n)$ for desirable outputs. The minimum values are defined as $x_i^{min}=0$ if $\mathrm{m}\mathrm{i}\mathrm{n}\left\{x_{ij}:j\in \left\{1,\dots ,n\right\}\right\}>0$, $x_i^{min}=-{\epsilon }_i$ if $\mathrm{m}\mathrm{i}\mathrm{n}\left\{x_{ij}:j\in \left\{1,\dots ,n\right\}\right\}=0$, and $x_i^{min}=\mathrm{m}\mathrm{i}\mathrm{n}\left\{x_{ij}:j\in \left\{1,\dots ,n\right\}\right\}(1+{\epsilon }_i)$ if $\mathrm{m}\mathrm{i}\mathrm{n}\left\{x_{ij}:j\in \left\{1,\dots ,n\right\}\right\}<0$, and similarly, $y_r^{min g}=0$ if $\mathrm{m}\mathrm{i}\mathrm{n}\left\{y_{rj}^{min g}:j\in \left\{1,\dots ,n\right\}\right\}>0$, $y_r^{min g}=-{\tau }_r$ if $\mathrm{m}\mathrm{i}\mathrm{n}\left\{y_{rj}^{min g}:j\in \left\{1,\dots ,n\right\}\right\}=0$, $y_r^{min g}=\mathrm{m}\mathrm{i}\mathrm{n}\left\{y_{rj}^{min g}:j\in \left\{1,\dots ,n\right\}\right\}(1+{\tau }_r)$ if $\mathrm{m}\mathrm{i}\mathrm{n}\left\{y_{rj}^{min g}:j\in \left\{1,\dots ,n\right\}\right\}<0$, where ${\epsilon }_i$ and ${\tau }_r$ are small positive numbers. Hence, we solve the following model to assess the relative efficiency of each steel company.

$$\mathrm{m}\mathrm{i}\mathrm{n} {\rho }_o^{sbm}={\displaystyle \frac{1-\frac{1}{m}\sum _{i=1}^m\frac{s_i^{-}}{{\overline{x}}_{io}}}{1+\frac{1}{s} \sum _{r=1}^s\frac{s_r^{+}}{{\overline{y}}_{ro}^g}}}$$

$$\mathrm{s}.\mathrm{t}. {\sum }_{j=1}^n{\lambda }_j{\overline{x}}_{ij}={\overline{x}}_{io}-s_i^{-} i=1,\dots ,m$$

$${\sum }_{j=1}^n{\lambda }_j{\overline{y}}_{rj}^g={\overline{y}}_{ro}^g+s_r^{+} r=1,\dots ,s$$

(2)

$${\lambda }_j\ge 0,s_i^{-}\ge 0,s_r^{+}\ge 0$$

The efficiency score ${\rho }_o^{sbm}$, like ${\theta }_{0 }$, ranges from 0 to 1, where a value of 1 indicates that a steel firm is efficient and values less than 1 denote inefficiency. To resolve the issue of efficiency ties, i.e., multiple steel firms with ${\rho }_o^{sbm}$ = 1, Super SBM model by Tone [47] can be adopted [48]. Thus, we employ the following Super SBM model to rank and discriminate among these efficient steel firms.

$$\mathrm{m}\mathrm{i}\mathrm{n} {\rho }_o^{sup}={\displaystyle \frac{1+\frac{1}{m}\sum _{i=1}^m\frac{s_i^{+}}{{\overline{x}}_{io}}}{1-\frac{1}{s} \sum _{r=1}^s\frac{s_r^{-}}{{\overline{y}}_{ro}^g}}}$$

$$\mathrm{s}.\mathrm{t}. {\sum }_{j=1,\ne o}^n{\lambda }_j{\overline{x}}_{ij}\le {\overline{x}}_{io}+s_i^{+} i=1,\dots ,m$$

$${\sum }_{j=1,\ne o}^n{\lambda }_j{\overline{y}}_{rj}^g\ge {\overline{y}}_{ro}^g-s_r^{-} r=1,\dots ,s$$

(3)

$${\lambda }_j\ge 0,s_i^{+}\ge 0,{\overline{y}}_{ro}^g\ge s_r^{-}\ge 0$$

where ${\rho }_o^{sup}$ ranges from 1 upwards, and $s_i^{+}$ and $s_r^{-}$ represent the residual advantages by which an efficient steel firm outperforms the other steel firms in the ith input and the rth desirable output, respectively.

4. Sample and Data Collection

The sample comprised 30 steel firms listed on the Taiwan Stock Exchange. Based on the steel industry value chain information disclosed on the Industry Value Chain Information Platform (https://ic.tpex.org.tw) (accessed on 2 April 2025), established by the Taiwan Stock Exchange and the Taipei Exchange, these companies were systematically classified into upstream (US), midstream (MS), and downstream (DS) segments. The US segment is primarily responsible for supplying minimally processed materials such as billets, slabs, and ingots, the MS segment transforms these materials into intermediate materials, and the DS segment manufactures a diverse range of products tailored to various application needs. Each firm is assigned a unique code based on its supply chain segment (e.g., US01, MS01, DS01) used throughout the study.

Table 1. Sample steel firms in Taiwan.

Stock Code	Firm Name	Location	Supply Chain Segment	Firm Code
2002	China Steel	Kaohsiung City, Taiwan	Upstream	US01
2006	Tung Ho Steel	Taipei City, Taiwan	Upstream	US02
2007	Yieh Hsing	Kaohsiung City, Taiwan	Midstream	MS01
2008	Kao Hsing Chang Iron & Steel	Kaohsiung City, Taiwan	Midstream	MS02
2009	First Copper Technology	Kaohsiung City, Taiwan	Midstream	MS03
2010	Chun Yuan Steel	New Taipei City, Taiwan	Midstream	MS04
2012	Chun Yu	Kaohsiung City, Taiwan	Midstream	MS05
2013	China Steel Structure	Kaohsiung City, Taiwan	Downstream	DS01
2014	Chung Hung Steel	Kaohsiung City, Taiwan	Midstream	MS06
2015	Feng Hsin Steel	Taichung City, Taiwan	Upstream	US03
2017	Quintain Steel	Tainan City, Taiwan	Midstream	MS07
2020	Mayer Steel Pipe	Taipei City, Taiwan	Midstream	MS08
2022	Tycoons Group	Kaohsiung City, Taiwan	Midstream	MS09
2023	Yieh Phui	Kaohsiung City, Taiwan	Midstream	MS10
2024	Chih Lien	Taoyuan City, Taiwan	Downstream	DS02
2025	Chien Shing Stainless Steel	Tainan City, Taiwan	Midstream	MS11
2027	Ta Chen Stainless Pipe	Tainan City, Taiwan	Midstream	MS12
2028	Wei Chih Steel	Tainan City, Taiwan	Upstream	US04
2029	Sheng Yu Steel	Kaohsiung City, Taiwan	Midstream	MS13
2030	Froch	Yunlin County, Taiwan	Midstream	MS14
2031	Hsin Kuang Steel	New Taipei City, Taiwan	Midstream	MS15
2032	Sinkang	New Taipei City, Taiwan	Midstream	MS16
2033	Chia Ta World	Tainan City, Taiwan	Downstream	DS03
2034	YC Inox	Changhua County, Taiwan	Midstream	MS17
2038	Hai Kwang	Kaohsiung City, Taiwan	Midstream	MS18
2069	Yuen Chang Stainless Steel	Kaohsiung City, Taiwan	Midstream	MS19
2211	Evergreen Steel	Taipei City, Taiwan	Downstream	DS04
3004	National Aerospace Fasteners	Taoyuan City, Taiwan	Downstream	DS05
5007	San Shing Fastech	Tainan City, Taiwan	Downstream	DS06
9958	Century Iron and Steel	Taoyuan City, Taiwan	Downstream	DS07

summarizes the sample steel firms, including their stock codes, names, locations, supply chain segments (US, MS, DS), and assigned firm codes.

For analytical clarity, this study rests on several simplifying assumptions. First, all steel firms are deemed subject to the carbon fee, regardless of whether their emissions exceed the threshold. Second, in the absence of complete Scope 3 emissions data, we proxy total emissions by adding up Scope 1 direct and Scope 2 indirect emissions. Finally, the carbon fee is estimated as total emissions multiplied by an official collection rate of NT$300 per ton and an adjustment factor of 0.2, both set by Taiwan’s Ministry of Environment, with preferential rates and offset quotas excluded.

Two evaluation frameworks are adopted for analysis, one considering carbon fees (i.e., carbon fee scenario) and the other without considering carbon fees (i.e., traditional scenario). In the traditional scenario, the input variables include property, plant, and equipment (PPE), number of employees, and operating expenses. The desirable outputs are operating revenue and operating profit. In the carbon fee scenario, the input variables consist of PPE, number of employees, operating expenses, and estimated carbon fees, while the output variables are operating revenue and operating profit, further deducted by carbon costs. Except for the carbon fees, all remaining input and output variables are commonly employed in DEA studies of firm performance, e.g., Ray and Kim [22], Ma et al. [23], Yang and Choi [24], Debnath and Sebastian [25], He et al. [27], Kim et al. [29], Kim et al. [30], Fukuyama et al. [36], Choi et al. [38].

This study uses the latest available 2024 steel firm data, which were collected and compiled in 2025. Data on PPE, number of employees, operating expenses, operating revenue, and operating profit were obtained from the Taiwan Economic Journal (TEJ) (https://www.tejwin.com/en/) (accessed on 2 May 2025). Carbon emissions data, used to estimate carbon fees, were sourced from the Market Observation Post System (MOPS) (https://emops.twse.com.tw) (accessed on 16 July 2025).

Table 2. Descriptive statistics for the variables.

Supply Chain Segment	Statistic	Carbon Fees (NT$thousand)	Property, Plant, and Equipment (NT$thousand)	Number of Employees (No.)	Operating Expenses (NT$thousand)	Operating Revenue (NT$thousand)	Operating Profit (NT$thousand)
Upstream	Mean	467,983	107,580,986	3284	4,254,104	116,318,542	2,661,661
(n = 4)	Maximum	1,751,983	397,633,498	9632	13,269,169	360,535,714	5,704,942
	Minimum	14,042	4,226,820	387	179,858	10,196,132	376,970
	SD	856,265	193,461,538	4294	6,102,013	164,084,809	2,254,627
Midstream	Mean	4780	7,648,014	542	1,308,581	17,668,636	463,074
(n = 19)	Maximum	31,172	44,403,003	1500	10,941,106	90,398,484	6,112,121
	Minimum	53	358,030	80	48,899	1,058,326	−1,240,502
	SD	7553	11,703,967	432	2,625,514	24,092,936	1,471,389
Downstream	Mean	2803	4,424,981	530	383,790	8,154,638	1,179,388
(n = 7)	Maximum	14,338	17,157,127	1452	609,140	19,695,058	2,971,348
	Minimum	208	440,665	115	60,624	577,650	16,504
	SD	5131	5,790,056	449	231,014	7,131,892	1,257,652
Overall	Mean	66,079	20,220,369	905	1,485,533	28,602,024	923,359
(n = 30)	Maximum	1,751,983	397,633,498	9632	13,269,169	360,535,714	6,112,121
	Minimum	53	358,030	80	48,899	577,650	−1,240,502
	SD	318,741	71,973,685	1722	3,084,195	66,306,438	1,663,823

presents the descriptive statistics for the variables in 2024, including the mean, maximum, minimum, and standard deviation (SD), across the US, MS, and DS segments of the supply chain, as well as for the overall sample. This offers an overview of the central tendency and variability in the dataset. As shown, US firms demonstrate the largest scale in terms of PPE, with a mean value of approximately NT$107.6 billion. This figure is substantially higher than those observed in the MS (NT$7.6 billion) and DS (NT$4.4 billion) segments. Similar patterns are observed for other indicators, including the number of employees, operating expenses, operating revenue, and operating profit, all of which are considerably greater for US firms. These results reflect the higher capital intensity and larger operational scale characteristics of US firms. Consistently, the estimated carbon fees for US firms are also higher on average, likely due to their more energy-intensive production processes and consequently greater carbon emissions. It is important to note that the operating profit figures presented here are based on original data and do not reflect deductions for carbon fees. As shown by the minimum values in the MS and overall segments, some firms already recorded negative operating profits in 2024, indicating that operating losses had occurred even before accounting for carbon fees. Once carbon fees are incorporated, negative profits become more common in the sample. This situation reveals the practical necessity of applying models that can properly deal with negative data.

5. Results and Discussion

The efficiency analysis results for 30 steel firms under the traditional and carbon fee scenarios are summarized in

Table 3. Results of analysis under two scenarios.

Steel Firms	Traditional Scenario				Carbon Fee Scenario				Comparison
	SBM Score ${\mathit{\rho }}_{\mathit{o}}^{\mathit{s}\mathit{b}\mathit{m}}$	Super SBM Score ${\mathit{\rho }}_{\mathit{o}}^{\mathit{s}\mathit{u}\mathit{p}}$	Composite Score ${\mathit{\delta }}_{\mathit{o}}$	Rank	SBM Score ${\mathit{\rho }}_{\mathit{o}}^{\mathit{s}\mathit{b}\mathit{m}}$	Super SBM Score ${\mathit{\rho }}_{\mathit{o}}^{\mathit{s}\mathit{u}\mathit{p}}$	Composite Score ${\mathit{\delta }}_{\mathit{o}}$	Rank	Efficiency Change	Rank Change
US01	0.057642	-	0.057642	30	0.019014	-	0.019014	30	Decreased	Unchanged
US02	0.380949	-	0.380949	19	0.298134	-	0.298134	21	Decreased	Declined
US03	0.578329	-	0.578329	13	0.441671	-	0.441671	16	Decreased	Declined
US04	1	1.013787	1.013787	10	1	1.010061	1.010061	11	Decreased	Declined
MS01	0.189406	-	0.189406	28	0.172898	-	0.172898	28	Decreased	Unchanged
MS02	0.335183	-	0.335183	21	0.338393	-	0.338393	19	Increased	Improved
MS03	1	1.128864	1.128864	3	1	1.108518	1.108518	6	Decreased	Declined
MS04	0.268585	-	0.268585	24	0.277183	-	0.277183	23	Increased	Improved
MS05	0.339615	-	0.339615	20	0.327356	-	0.327356	20	Decreased	Unchanged
MS06	1	1.032727	1.032727	7	1	1.028015	1.028015	10	Decreased	Declined
MS07	0.24311	-	0.24311	25	0.20877	-	0.20877	27	Decreased	Declined
MS08	0.564157	-	0.564157	16	0.527047	-	0.527047	14	Decreased	Improved
MS09	0.779305	-	0.779305	12	0.676996	-	0.676996	13	Decreased	Declined
MS10	0.162941	-	0.162941	29	0.141578	-	0.141578	29	Decreased	Unchanged
MS11	1	1.11991	1.11991	4	1	1.106031	1.106031	7	Decreased	Declined
MS12	1	1.167897	1.167897	2	1	1.151558	1.151558	3	Decreased	Declined
MS13	0.474426	-	0.474426	18	0.412338	-	0.412338	17	Decreased	Improved
MS14	0.27908	-	0.27908	23	0.29486	-	0.29486	22	Increased	Improved
MS15	1	1.011209	1.011209	11	1	1.124636	1.124636	5	Increased	Improved
MS16	1	1.018897	1.018897	8	1	1.872449	1.872449	1	Increased	Improved
MS17	0.227885	-	0.227885	26	0.254988	-	0.254988	24	Increased	Improved
MS18	0.525486	-	0.525486	17	0.406267	-	0.406267	18	Decreased	Declined
MS19	1	1.05847	1.05847	5	1	1.043819	1.043819	9	Decreased	Declined
DS01	1	1.360718	1.360718	1	1	1.386502	1.386502	2	Increased	Declined
DS02	0.569669	-	0.569669	14	0.755185	-	0.755185	12	Increased	Improved
DS03	1	1.014992	1.014992	9	1	1.145818	1.145818	4	Increased	Improved
DS04	0.565703	-	0.565703	15	0.443439	-	0.443439	15	Decreased	Unchanged
DS05	0.212327	-	0.212327	27	0.216199	-	0.216199	26	Increased	Improved
DS06	0.282148	-	0.282148	22	0.249472	-	0.249472	25	Decreased	Declined
DS07	1	1.043417	1.043417	6	1	1.05742	1.05742	8	Increased	Declined

. For each firm, we report the SBM efficiency ${\rho }_o^{sbm}$ (derived from Model (2)), Super SBM efficiency ${\rho }_o^{sup}$ (derived from Model (3)), and composite efficiency ${\mathsf{\delta }}_o$ with rankings in each scenario. Since ${\rho }_o^{sbm}\in \left[\mathrm{0,1}\right]$ while ${\rho }_o^{sup}\ge 1$ and applies only to efficient firms with ${\rho }_o^{sbm}$ = 1, the composite efficiency measure is given by ${\mathsf{\delta }}_o={\rho }_o^{sbm}$ if ${\rho }_o^{sbm}<1$ and ${\mathsf{\delta }}_o={\rho }_o^{sup}$ otherwise. The last two columns of Table 3 display the changes in composite efficiency and ranking between the two scenarios.

In both scenarios, 11 of 30 firms are efficient (${\rho }_o^{sbm}$ = 1 and ${\rho }_o^{sup}$ > 1), while the remaining 19 are inefficient (${\rho }_o^{sbm}$ < 1). Despite these identical classification totals, notable differences remain. At the aggregate level, the mean SBM efficiency falls from 0.601 (traditional) to 0.582 (carbon fee), whereas the mean composite efficiency rises modestly from 0.634 to 0.65. To test scenario differences, the non-parametric Wilcoxon signed-rank tests (n = 30) were conducted separately for the paired SBM efficiency and composite efficiency scores. For SBM efficiency, the test result shows that the Z-value is 2.294 and the two-tailed p-value is 0.022, rejecting the null hypothesis of no scenario difference at the 5% significance level. This indicates that incorporating the carbon fee has a statistically significant impact on SBM efficiency. A directional (one-tailed) test, used to examine the hypothesis that SBM efficiency under the traditional scenario exceeds that under the carbon fee scenario, yields a p-value of 0.011, confirming a significant reduction in SBM efficiency. In contrast, for composite efficiency, the test yields a Z-value of 1.327 with a two-tailed p-value of 0.184, indicating no statistically significant difference at the 5% significance level. Accordingly, no one-tailed test was performed. Overall, the test results suggest that the carbon fee’s impact is concentrated on firms that were initially inefficient (${\rho }_o^{sbm}$ < 1), implying that the traditional scenario could provide a more lenient assessment of efficiency. This phenomenon is similar to the results of He et al. [27] and Choi et al. [38], which incorporate undesirable outputs and demonstrate that excluding undesirable outputs leads to an upward bias in steel firms’ efficiency scores. Hence, price-based carbon cost internalization and explicit modeling of emissions may function as complementary mechanisms with similar practical implications.

Most firms exhibit shifts in composite efficiency scores and associated rankings. We define ${∆}_E$ (composite efficiency change) as the carbon fee efficiency minus traditional efficiency, and ${∆}_R$ (ranking change) as the traditional rank minus the carbon fee rank to compare impacts of the carbon fee across the US, MS, and DS segments. Positive ${∆}_E$ and ${∆}_R$ indicate efficiency and ranking (joint) improvement, while negative ${∆}_E$ and ${∆}_R$ indicate joint deterioration. After accounting for the carbon fee, 19 firms (63.33%) experience a decrease in efficiency (${∆}_E<0$), whereas 11 firms (36.67%) record an increase (${∆}_E>0$). In terms of rankings, 11 firms (36.67%) move up (${∆}_R>0$), 14 firms (46.67%) move down (${∆}_R<0$), and 5 firms (16.67%) stay unchanged. Based on the joint signs of ${∆}_E$ and ${∆}_R$, Figure 1 maps the firms into four quadrants: Q1 (dual improvement, ${∆}_E>0,{∆}_R>0$), Q2 (efficiency decline and ranking improvement, ${∆}_E<0,{∆}_R>0$), Q3 (dual deterioration, ${∆}_E<0,{∆}_R<0$), and Q4 (efficiency gain and ranking decline, ${∆}_E>0,{∆}_R<0$). Quadrant allocation yields Q1 = 9, Q2 = 2, Q3 = 12, and Q4 = 2, plus five boundary firms with ${∆}_R=0$ (n = 30). The dominance of Q3 signals widespread joint deterioration, yet most rank improvements (9 of 11 in Q1) coincide with efficiency gains, with only 2 in Q2 occurring despite efficiency declines.

The US segment records average changes of ${∆}_E$ = −0.0655 and ${∆}_R$ = −1.5. All four firms (100%) experience a decrease in efficiency scores. Among them, firm US01 maintains its previous position, whereas the other three, namely firms US02, US03, and US04, also experience a decline in ranking, placing them in Q3. The joint deterioration rate (share of firms in Q3) is 75% (3/4), the highest across segments.

For the MS segment, despite a modest positive mean efficiency change ${∆}_E$ = 0.0288 with an average rank improvement ${∆}_R$ = 0.211, 13 of 19 firms (68.4%) demonstrate a decrease in efficiency scores. Among these firms, eight firms, i.e., MS03, MS06, MS07, MS09, MS11, MS12, MS18, and MS19, also lose rank, placing them in Q3 and yielding a joint deterioration rate of 42.1% (8/19). Three firms (MS01, MS05, and MS10) maintain their original ranks, and only two firms (MS08, MS13) improve their rankings despite the decline in efficiency, placing them in Q2. Six firms, i.e., MS02, MS04, MS14, MS15, MS16, and MS17, are grouped in Q1 with a dual improvement, and firms MS15 and MS16 strongly raise the segment mean. These results indicate that, under the carbon fee, the midstream segment exhibits a polarized pattern in which a minority of firms improve both efficiency and rank while most decline on both, implying that rank gains are rarely realized in the absence of actual efficiency improvement.

The DS segment posts average changes of ${∆}_E$ = 0.0293 and ${∆}_R$ = 0.286, mainly driven by the three firms, i.e., DS02, DS03, and DS05, in Q1 (42.9%) that simultaneously enhanced efficiency and ranking. Only two firms (28.6%), DS04 and DS06, experience efficiency declines. Of these, firm DS04’s efficiency falls while its ranking remains unchanged, and firm DS06 also loses ranking and is classified in Q3, yielding the lowest joint deterioration rate of 14.3% (1/7) across segments. Another two firms, DS01 and DS07, fall into Q4, indicating their pace of efficiency improvement was outstripped by peers.

Overall, the carbon fee exerts the greatest adverse impact on the US segment, a moderate and polarized impact on the MS segment, and the weakest impact on the DS segment. Emission concentration in core production processes led to uniform efficiency and ranking deterioration among US firms, except for one that held its competitive position. The carbon fee triggered polarization and competitive reshuffling in the MS segment. Some firms (notably MS15 and MS16) simultaneously improved efficiency and ranking, while the largest group experienced efficiency and ranking setbacks. DS firms, by contrast, benefited from lower emission intensity, achieving broad efficiency improvements, although rank gains remained limited.

Figure 2 depicts the distribution of composite efficiency scores for the US, MS, and DS segments under the two scenarios. Relative to the traditional scenario, the carbon fee increases efficiency score dispersion across all supply chain segments, as indicated by higher standard deviations, coefficients of variation, and wider ranges. The standard deviation (coefficient of variation) rises from 0.4 (0.788) to 0.417 (0.944) in the US segment, 0.382 (0.609) to 0.479 (0.729) in the MS segment, and 0.428 (0.593) to 0.463 (0.617) in the DS segment. These results suggest that the carbon fee widens inter-firm dispersion, thereby potentially enhancing the discriminatory power of efficiency assessment. Additionally, the median efficiency retains the same ordering US < MS < DS in both scenarios, with medians of 0.480, 0.525, and 0.570 under the traditional scenario and 0.37, 0.412, and 0.755 under the carbon fee. All of these scores are below 1, indicating that there is room for improvement among firms in all three segments of the supply chain. This consistent ordering implies that the US firms require the most substantial adjustments, followed by those in the MS segment, while the DS firms require the least adjustment.

Table 4. Potential adjustment for the 30 steel firms under the carbon fee scenario.

Steel Firms	Status	Carbon Fees (%)	Property, Plant, and Equipment (%)	Number of Employees (%)	Operating Expenses (%)	Operating Revenue (%)	Operating Profit (%)
US01	Inefficient	97.40	79.75	0.00	0.00	0.00	5660.29
US02	Inefficient	88.29	54.17	0.00	44.86	0.00	156.67
US03	Inefficient	93.65	60.87	0.00	18.22	0.00	57.27
US04	Efficient	0.00	0.00	0.00	4.02	0.00	0.00
MS01	Inefficient	60.01	75.79	32.88	0.00	0.00	468.95
MS02	Inefficient	74.84	59.35	6.94	0.00	182.49	0.00
MS03	Efficient	0.00	0.00	0.00	43.41	0.00	0.00
MS04	Inefficient	74.44	29.62	0.00	5.37	0.67	323.47
MS05	Inefficient	89.45	46.39	0.00	67.10	0.00	101.00
MS06	Efficient	0.00	0.00	0.00	11.21	0.00	0.00
MS07	Inefficient	73.62	71.72	0.00	44.35	282.09	21.61
MS08	Inefficient	46.80	0.00	3.13	25.43	107.98	0.00
MS09	Inefficient	61.53	11.53	0.00	41.24	0.00	11.01
MS10	Inefficient	55.67	34.34	0.00	18.75	0.00	828.53
MS11	Efficient	0.00	0.00	17.83	9.52	0.00	6.81
MS12	Efficient	0.00	0.00	60.62	0.00	0.00	0.00
MS13	Inefficient	60.42	11.07	0.00	48.86	0.00	139.11
MS14	Inefficient	79.85	62.94	0.00	55.25	0.00	142.49
MS15	Efficient	15.00	0.00	34.85	0.00	0.00	0.00
MS16	Efficient	68.30	0.00	0.00	0.00	0.00	74.95
MS17	Inefficient	77.28	75.56	0.00	60.19	0.00	166.63
MS18	Inefficient	93.14	75.30	32.72	0.00	0.00	44.71
MS19	Efficient	0.00	0.00	17.53	0.00	0.00	0.00
DS01	Efficient	0.00	0.00	0.00	0.00	55.75	0.00
DS02	Inefficient	29.43	51.05	17.45	0.00	0.00	0.00
DS03	Efficient	0.00	0.00	0.00	4.06	0.00	23.68
DS04	Inefficient	88.52	45.44	0.00	22.33	74.80	0.00
DS05	Inefficient	15.93	43.08	0.00	21.73	514.45	23.91
DS06	Inefficient	57.95	13.88	51.79	0.00	334.75	19.19
DS07	Efficient	0.00	0.00	22.97	0.00	0.00	0.00
Average		46.72	30.06	9.96	18.20	51.77	275.68

presents the efficiency status of 30 firms, along with the potential adjustment ratios for various indicators, including carbon fees, PPE, number of employees, operating expenses, operating revenue, and operating profit. These ratios are calculated by dividing the optimal slack value of each variable by its range.

For inefficient firms, the optimal slack values for each variable are obtained by solving the SBM model (2), and the resulting adjustment ratios (in percent) represent required input contractions or output expansions for improvement. For example, for firm US01, the ratios indicate that carbon fees and PPE should be reduced by 97.40% and 79.75%, respectively, while no adjustment is needed for the number of employees, operating expenses, or operating revenue. However, operating profit should be increased by a substantial 5660.29%, reflecting a considerable gap from the efficient frontier. Similarly, US02 requires reductions in carbon fees (88.29%), PPE (54.17%), and operating expenses (44.86%), as well as an increase in operating profit (156.67%). In contrast, for efficient firms, the optimal slack values are derived from the Super SBM model (3), and the adjustment ratios reflect the residual advantage relative to the efficient frontier, indicating how much an input can be increased or outputs reduced without compromising efficiency status. For instance, firm US04 could increase its operating expenses by 4.02% without losing efficiency, while all other indicators require no adjustment. Another efficient firm, MS11, shows the main advantage in the number of employees (17.83%), operating expenses (9.52%), and operating profit (6.81%). Notably, MS16 exhibits a particularly high advantage in carbon fees (68.30%) and operating profit (74.95%), suggesting a unique position relative to the efficient frontier constructed by the remaining firms.

The last row of Table 4 shows that, on average across all steel firms, carbon fees (46.72%) exhibit the greatest potential for adjustment among input variables, followed by PPE (30.06%), operating expenses (18.20%), and number of employees (9.96%). For the output variables, the greatest potential for adjustment is observed in operating profit (275.68%), followed by operating revenue (51.77%). This finding reveals that carbon fees and operating profit are, respectively, the most critical input and output variables influencing the efficiency scores of steel firms. Therefore, Taiwanese steel firms, especially those identified as inefficient, could consider adopting various carbon reduction measures, such as increasing the use of scrap and electric arc furnace steelmaking, developing low-carbon blast furnace technologies, and implementing carbon capture and storage (CCS) systems [49,50,51] to not only reduce carbon emissions, but also help lower carbon-related costs and accelerate the transition toward a more sustainable steel industry.

Figure 3 illustrates the segment-level average adjustment ratios (in percent) for input and output variables across the US, MS, and DS segments, grouped by efficiency status. Each colored bar represents a specific variable with its percentage value at the bar end. Clearly, the US and MS segments have substantial operating profit improvement potential that may be attributable to high carbon intensity, incomplete capital utilization, a heavy operating cost base, and limited market development. Inefficient US firms require pronounced reductions in carbon fees (93.12%) and PPE (64.93%), and a moderate contraction in operating expenses (21.03%), with no adjustment in employee count or operating revenue. Efficient US firms have virtually no residual advantage, with only a 4.02% allowable increase in operating expenses. Compared with other segments, the US segment shows the most extreme simultaneous carbon and capital drawdown requirement. In the MS segment, inefficient MS firms confront major carbon fee (70.59%) and PPE (46.13%) reductions and the largest operating expense contraction across segments (30.54%), while also needing to raise operating revenue (47.77%) and adjust employee count only modestly (6.31%). Efficient MS firms retain notable residual advantage in carbon fees (11.90%), employee count (18.69%), operating expenses (9.16%), and operating profit (11.68%), giving flexibility across carbon cost profile, workforce deployment, and resource allocation. Relative to other inefficient peers, inefficient DS firms show a more balanced set of reductions in carbon fees (47.96%), PPE (38.36%), employee count (17.31%), and operating expenses (11.02%), along with increases in operating revenue (231.00%) and operating profit (10.78%). For efficient DS firms, the most pronounced residual advantage resides in operating revenue (18.58%) and operating profit (7.89%), reflecting stronger market performance and profitability compared to other efficient peers.

6. Conclusions

Against the backdrop of the global push toward net-zero emissions, Taiwan is set to bid farewell to the era of free carbon emissions by levying a carbon fee. The steel industry, as a major carbon-emitting and energy-intensive sector, is poised to face unprecedented challenges under this forthcoming carbon pricing policy. Therefore, exploring and simulating the impact of carbon fee implementation on the steel industry is not only a timely issue but also a critical one for policymakers and industry stakeholders.

This study applies SBM and Super SBM models, which allow for negative data, to evaluate the efficiencies of 30 Taiwanese steel companies under two scenarios: one without carbon fees and one with carbon fees implemented. The results indicate that it is essential to incorporate the carbon fees into the efficiency evaluation of steel firms’ operations. Accounting for the carbon fee mitigates the overestimation of inefficient firms’ SBM efficiencies and widens cross-firm efficiency dispersion for stronger discriminatory power. Also, it triggers broad efficiency and ranking shifts, with the adverse impact greatest upstream, moderate in midstream, and weakest downstream. The analysis of potential adjustments in slack shows that, overall, carbon fees and operating profit are key variables leading to inefficiency. To improve operating performance, upstream firms need to greatly reduce expenditures on carbon fees and capital, as well as enhance operating profit. Meanwhile, midstream and downstream firms should further strengthen operating revenue, tighten operating expenses, and optimize human resources, in addition to addressing carbon fees and capital expenditures. It is important to note that the efficiency results obtained in this study are based on the preliminary carbon fee rates set by Taiwan’s Ministry of Environment, without considering any preferential measures or offset quotas. This limitation may affect the generalizability of our findings, as the actual impacts will ultimately depend on the finalized details of future carbon fee policies in Taiwan.

Incorporating carbon fees into efficiency evaluation can help steel firms better respond to the forthcoming challenges of carbon pricing and develop effective business strategies for operational improvement. The research framework of this study can also be applied to examine the impacts of carbon pricing policies on other industries, such as petrochemical, electronics, cement, and construction. As carbon pricing policies continue to evolve in Taiwan, future research could further refine the analysis by considering dynamic policy changes, including broader datasets, and applying more advanced efficiency assessment models, such as network DEA and dynamic DEA, for a more comprehensive evaluation.