Airline Carbon Emission Efficiency Study: Static and Dynamic Perspectives

Abstract

Amid the rapid growth of the aviation sector, carbon reduction presents a significant challenge for airlines. This study investigates the structural characteristics and dynamic evolution of carbon emission efficiency among 18 global airlines from 2015 to 2021 using a two-stage super-efficient slack-based measure model (SBM) and an SBM-based Hicks–Moorsteen productivity index, incorporating absolute β-convergence tests. Key findings include the following: (1) The overall mean static efficiency of the airlines ranged from 0.225 (American Airlines) to 0.662 (Singapore Airlines), with an industry-wide average of 0.44. (2) Dynamic productivity change also exhibited significant variation: the overall mean superefficient SBM-based Hicks–Moorsteen (HM) productivity index was 0.962, but it dropped sharply to 0.526 in 2019–2020 due to the COVID-19 pandemic. After 2020, several airlines demonstrated significant recovery, with Emirates and Singapore Airlines achieving dynamic productivity change indices above 1.5. (3) In 16 out of 18 airlines, operational efficiency exceeded production efficiency, highlighting the importance of technological improvements in production. (4) Limited technological progress was identified as the main factor behind efficiency declines, while absolute β-convergence indicated that inefficient airlines are gradually catching up with efficient peers. These findings provide insights for airlines and policymakers in designing targeted carbon reduction strategies and promoting sustainable aviation development. The empirical scope of this study is limited to 18 major global airlines over the period 2015–2021. Due to data availability constraints, the sample does not fully cover all regions or low-cost carriers. The Hicks–Moorsteen index and its EC/TC components are used for interpretative and heuristic purposes only and should not be understood as a strict mathematical decomposition within the two-stage network SBM framework.

1. Introduction

Excessive carbon dioxide (CO₂) emissions are considered to be a major contributor to global warming, an issue that has attracted close global attention [1]. As a significant source of CO₂ emissions, the aviation industry has been continuously monitored by international environmental organizations. According to the International Council on Clean Transportation (ICCT), the aviation industry emitted approximately 918 million tons of CO₂ in 2018, accounting for 2.4% of total global emissions, a 32% increase from five years ago [2]. According to the Boeing Commercial Market Outlook 2023–2042, global air traffic demand is expected to grow steadily over the next two decades, which will exert continued upward pressure on aviation carbon emissions. Existing studies further estimate that global aviation CO₂ emissions could reach approximately 1.8–2.1 billion tons by 2030, corresponding to an average annual growth rate of around 3%, although such figures are typically derived from traffic growth projections combined with emission intensity assumptions rather than directly reported by Boeing [3]. According to the 2023 forecast by the International Energy Agency (IEA), aviation carbon emissions will increase by 300% by 2050 compared to 2019 [4]. While industry and governments have been focusing on reaching net-zero carbon dioxide (CO₂) emissions by 2050, less attention has been paid to the role of short-lived climate pollutant (SLCP) mitigation in aligning aviation with the Paris Agreement [5]. Hence, reaching net-zero CO₂ emissions by 2050 is a critical challenge for aviation, its value chain, and its stakeholders [6]. This continuously growing trend has caused concern among governments and the public, and thus, controlling and reducing aviation carbon emissions is increasingly becoming a pressing issue [7]. At its 41st session, the International Civil Aviation Organization (ICAO) adopted an initiative called the Long-Term Aspirational Goal (LTAG), which calls on governments to take large-scale measures to reduce emissions and expand the use of sustainable fuels to push the aviation industry toward a zero-carbon emissions goal by 2050 [8]. This initiative poses an unprecedented challenge for the global aviation industry, requiring practical initiatives by all parties in the industry to realize the vision of zero carbon emissions.

To achieve this goal, airlines need to control CO₂ emissions to achieve sustainable development, so scholars have performed much empirical research on the carbon emission efficiency of civil aviation transportation [9]. Static carbon emission efficiency is the level of efficiency of carbon emissions generated by a decision-making unit (DMU) in its production process relative to its output at a given point in time, which reflects the performance of that DMU in improving energy efficiency under given technological and resource conditions [10]. In contrast to the focus on static efficiency, dynamic productivity change focuses more on evolution and continuous improvement over the long term, focusing on how DMUs can continuously reduce their overall carbon emissions through the adoption of technological innovations or management changes [11]. Although several studies have examined airline environmental efficiency using either static DEA models or dynamic productivity indices, relatively fewer studies integrate both perspectives within a unified analytical framework. To fill this research gap, this paper investigates the static and dynamic carbon emission efficiency of 18 major global airlines during 2015–2021 by combining a two-stage super-efficiency network SBM model and an SBM-based Hicks–Moorsteen (HM) productivity index.

The scope and limitations of this study are clearly defined. The sample covers 18 major full-service airlines across regions, but low-cost carriers and some regions are not fully included due to data availability constraints. The period 2015–2021 does not include the latest years after 2021. The Hicks–Moorsteen index and its EC and TC components are used only for interpretative and heuristic purposes. Since the decomposition was originally developed for single-stage DEA models, it does not strictly apply to the two-stage network structure, and no strict mathematical decomposition is claimed.

2. Materials and Methods

2.1. Literature Review

2.1.1. Static Carbon Efficiency Studies

Early research on airline efficiency often relied on single-factor indicators, such as carbon productivity, defined as output or revenue per unit of carbon emissions [12]. For example, Jung et al. examined the impact of a carbon emissions trading scheme on firms’ carbon productivity [13]. The above studies used the single-factor carbon efficiency indicator to study carbon emission efficiency, but the single-factor carbon efficiency can only reflect the carbon emissions per unit of output, which is not comprehensive enough to measure the carbon emission efficiency of an enterprise or an economy as a whole [14].

To overcome this limitation, scholars increasingly adopted total-factor carbon emission efficiency, which considers multiple inputs and outputs simultaneously. Based on data envelopment analysis (DEA), this approach assesses the overall relationship between resource use, emissions, and outputs [15]. For instance, Chen and Mu studied the extent to which the total factor carbon efficiency of 30 provinces in China is affected by carbon trading policies [16], and Zhou and Qi found that to improve the total factor green energy efficiency, it is necessary to start by encouraging the technological innovation of enterprises [17].

In the airline industry, DEA-based studies have been widely applied. Schefczyk pioneered the use of DEA to assess the operational performance of 15 international airlines [18]. In addition, Seyedalizadeh et al. innovatively integrated principal component analysis with Q-methodology to construct an improved neutral cross-efficiency model [19]. By incorporating positive and negative output indicators such as flight punctuality rates and delay durations, they further addressed the strong subjectivity in weight selection of traditional DEA models, providing a more precise analytical framework for airline efficiency evaluation.

Subsequent studies extended this approach by incorporating carbon emissions as undesirable outputs. Chang et al. employed the slack-based measure (SBM) DEA model to assess the environmental efficiency of 27 global airlines [20], while Wang et al. applied the global SBM model to evaluate 13 Chinese carriers [21]. These works demonstrated that including CO₂ emissions significantly alters efficiency rankings and provides more realistic insights into environmental performance.

More recently, scholars have highlighted the complexity of airline operations and argued that a single-stage DEA framework may oversimplify reality. Network DEA models, particularly two-stage SBM approaches, allow the production process to be divided into phases such as production and operations. Chen et al. investigated the efficiency of CO₂ emissions by dividing the operation process of Chinese airlines into production and profit stages using the two-stage network SBM method [22]. Cui and Li also used a network SBM model to more accurately assess the impact of CO₂ emissions on airline efficiency by dividing the energy efficiency of 22 international airlines into operational and carbon reduction phases [23]. Yang et al. proposed a fuzzy common weight additive network DEA model, which addressed the issues of shared resources and undesirable outputs by dividing airline operations into production and service stages, providing a more nuanced framework for efficiency assessment [24]. Building on this multi-stage analytical framework, Ganji et al. integrated prospect theory into a double-frontier cross-efficiency model, addressing decision-makers’ risk preferences often overlooked in traditional DEA approaches [25]. Ganji et al. addressed the decision-makers’ risk preferences and subjective perceptions often overlooked in traditional DEA approaches. This method was applied to 17 Iranian airlines, revealing significant differences in efficiency rankings when pessimistic and optimistic standpoints were considered [26]. See et al. further extended this line of research by developing a dynamic network DEA framework that integrates natural and managerial disposability concepts. By analyzing 24 global airlines from 2017 to 2019, their study revealed that efficiency levels under managerial disposability are significantly higher, highlighting the critical role of proactive environmental regulation in driving operational and environmental performance improvements within the aviation industry [27]. Yu and Rakshit further developed a DEA bargaining model that integrates undesirable outputs, enabling airlines to set optimal carbon reduction targets while maintaining operational efficiency. This approach, which was validated using data from major global carriers, provides a practical tool for balancing environmental performance and business objectives [28]. These studies suggest that decomposing operations into multiple stages yields richer managerial insights.

2.1.2. Dynamic Carbon Productivity Change Study

Dynamic productivity change refers to the variation in total factor productivity (TFP) of airlines over time, and it is often analyzed using indicators such as efficiency change (EC) and technological change (TC) to identify potential drivers of productivity evolution. This study does not measure ‘dynamic efficiency’ in the strict DEA sense (which requires intertemporal linkages of inputs/outputs), but focuses on tracking productivity fluctuations and their sources using a superefficient SBM-Hicks–Moorsteen (HM) productivity index. While static efficiency provides a snapshot at a given point in time, it does not capture long-term trends. To address this, researchers have developed dynamic measures of carbon performance, most notably through Malmquist-type indices. Lee et al. used the Luenberger index in their study to incorporate CO₂ emissions into an input-output framework to assess the productivity of 34 international airlines between 2004 and 2011 [29]. Scotti and Volta used the Malmquist-Luenberger index to assess changes in the carbon efficiency of 18 major European airlines from 2000 to 2010 [30]. Liu et al. propose a global Malmquist carbon performance index that utilizes the production frontier surface to assess the dynamics of total factor carbon efficiency in time series [9]. Yang and Guo further combined the super-efficiency SBM model and GML index to measure the carbon emission efficiency of 6 Chinese listed airlines from 2011 to 2019; the results showed that the carbon emission efficiency of China’s aviation enterprises a showed “U”-shaped trend of first decreasing and then increasing during the sample period [31]. To address the defect of slack variable neglect in the traditional DEA model, Tone [32] first proposed the slack-based measure (SBM) mode to measure the carbon emission efficiency of airlines. This model directly addresses input redundancy and insufficient output by introducing slack variables, which solves the bias problem of the traditional Charnes–Cooper–Rhodes (CCR) model that only measures efficiency from a radial perspective. This method has been used to study the evolution of Chinese airlines’ carbon performance, demonstrating both regional disparities and evidence of convergence. Nevertheless, the standard Malmquist index has limitations: it can only compare the same decision-making unit (DMU) across different time periods and cannot directly rank multiple DMUs simultaneously. This hybrid approach has become increasingly popular in airline studies, as it integrates the advantages of SBM in handling undesirable outputs with the ability of Malmquist indices to track changes over time.

2.1.3. Research Gaps and Contributions

In summary, existing literature on airline carbon emission efficiency falls into two streams: (1) static studies that evaluate efficiency at a given point in time using DEA or SBM, and (2) dynamic studies that track efficiency changes using Malmquist-type indices. Static approaches excel in identifying operational inefficiencies across airlines, while dynamic approaches reveal trends and the role of technological progress. However, relatively few studies combine static and dynamic perspectives within a unified framework.

Moreover, although DEA/SBM-based methods and dynamic productivity indices have been applied, prior research often focuses on either aggregate efficiency or a single operational stage. Less attention has been given to a two-stage framework that separates production efficiency (capacity building) from operational efficiency (service delivery), even though such a distinction provides valuable insights for airline management. Cooper et al. [33] defined slack variables as the core elements that reflect the over-investment of inputs and the under-achievement of output targets, providing a systematic basis for the two-stage framework to identify inefficiencies in both production and operational processes.

Finally, while much of the literature examines long-term trends, fewer studies explicitly account for external shocks such as the COVID-19 pandemic. These developments have fundamentally altered the landscape of airline operations and carbon management, highlighting the need for updated empirical evidence.

This study contributes to the literature in three ways. First, it jointly examines static and dynamic carbon emission efficiency for 18 major international airlines, providing a more holistic picture of performance. Second, it applies a two-stage superefficient SBM model, separating production and operational phases, thus offering detailed insights into efficiency drivers. Third, it incorporates the superefficient SBM-based Hicks–Moorsteen (HM) index to analyze dynamic changes between 2015 and 2021, a period covering both pre-pandemic growth and the COVID-19 shock, and further applies β-convergence tests to assess long-term trends across airlines.

2.2. Methodology

2.2.1. Input-Output Indicator Selection

The selection of indicators for inputs and outputs of some existing studies on the efficiency of civil aviation enterprises is shown in

Table 1. Input-output selection in airline efficiency evaluation.

Study	Method	Stage 1	Stage 2
Cui and Li 2016 [23]	Single-stage	Input: AF (aviation fuel), NE (number of employees) Output: R (Revenue), GHG	…
Yang et al., 2024 [24]	Two-stage fuzzy common weight additive network DEA with Z-number	Input: Aviation fuel, labor; Output: Available seat kilometer	Input: Available seat kilometers; Output: Revenue
Ganji et al., 2024 [25]	Network cross-efficiency DEA with regret theory	Input: Operational inputs (e.g., fuel, labor cost); Output: Available seat kilometers (ASK)	Input: Available seat kilometers (ASK); Output: Revenue/profit
Yu and Rakshit 2023 [28]	DEA-based Nash bargaining model with weakly disposable undesirable outputs	Input: Aviation fuel, labor Output: Turnover volume, CO2 emissions	…
Gramani 2012 [34]	Two-stage: operation, sales	Input: Aircraft cost, cost per ASK (available seat kilometers), wages, salaries and benefits Output: RPK (revenue passenger kilometers)	Input: The inverse of the efficiency value of the previous period. Output: Revenue, income from flights
Tan and Chen 2011 [35]	Two-stage: production, service	Input: Operational expenses (OPEX), AF Output: Flight frequency, mileage, flight time	Input: Flight frequency, flight miles, flight time Output: Passenger traffic, passenger turnover, cargo traffic, cargo turnover
Lu et al., 2012 [36]	Two-stage: production, sales	Input: OPEX, NE, total seating, maintenance costs, equipment costs Output: ASK, available ton kilometers	Input: ASK, available ton kilometers Output: RPK, nonpassenger revenue
Duygun et al., 2016 [37]	Two-stage: production, sales	Input: Fuel costs, fixed assets, bonuses, salaries, other operating costs Output: ASK, available ton kilometers	Input: ASK, available ton-kilometers, cost of goods sold Output: revenue ton-kilometer, RPK

. The use of the network DEA model to evaluate the efficiency of airlines typically encompasses the production stage, the operational stage, the sales stage and the service stage.

This paper focuses on the impact of carbon emissions in the internal operations of civil aviation companies and therefore categorizes the static efficiency of airlines into two key dimensions: production efficiency and operational efficiency. Based on the studies listed in Table 1, Figure 1 shows how this research divides the airline’s operation process into production and operational activities. In the production phase, resources (AF, NE) should be fully utilized to increase transportation capacity (ASK),as summarized in

Table 2. Airline inputs and outputs in two stages.

Stage	Input	Desirable Output	Undesirable Output
Production stage	AF NE	ASK
Operation stage	ASK OPEX	RPK R	CO2 emissions (CEs)

. Efficient production capacity means producing as much passenger transport as possible with the expected available resources [38]. In the operational stage, ASK from the previous stage is treated as an intermediate input, while operational expenses (OPEX) are introduced to capture the scale of operational resource use. Compared with fleet size (a stock variable), OPEX represents a flow-based measure of resource consumption, making it more consistent with DEA modeling principles and better suited to capture operational scale and intensity. The desirable outputs are RPK and operating revenue, while CO₂ emissions are treated as the undesirable output.

This paper uses a two-stage superefficient network SBM to assess the static carbon emission efficiency of airlines and applies the superefficiency SBM-based Hicks–Moorsteen (HM) index to assess the dynamic carbon emission efficiency of airlines. Section 2.2.2 and Section 2.2.3 explain the model construction specifically.

2.2.2. Two-Stage Superefficiency Network SBM Model with Undesirable Outputs

Considering the heterogeneity among the 18 airlines in terms of scale, business models (full-service/low-cost), and regional market characteristics, this study incorporates the variable returns to scale (VRS) assumption into the two-stage super-efficiency network SBM model to more accurately measure pure technical efficiency and avoid the interference of scale differences on efficiency evaluation. The data envelopment analysis DEA model, proposed by Charnes et al. [39], is a management tool for evaluating the efficiency of decision-making units with multiple inputs and multiple outputs. It has since been widely applied in diverse fields, including production management, environmental governance, and education. However, this traditional DEA model ignores slack variables, i.e., waste that may exist in the actual production process that a firm may have [40], and does not take into account that certain outputs are not expected in the production process. In addition, since the model focuses only on radial distance, it is possible that it overestimates the efficiency of firms [41]. However, both traditional DEA and single-stage SBM models treat the production process as a black box by ignoring its internal structural divisions (e.g., production and operational phases). This simplification may limit the accuracy of efficiency evaluation for complex production systems such as airlines, where intermediate outputs and inter-stage linkages play a critical role [42]. In this context, Tone and Tsutsui [43] proposed the Network SBM approach, which breaks the black box of traditional DEA models. This approach can handle intermediate products and inter-phase linkages, enabling more accurate DMU efficiency evaluation and phase-specific efficiency analysis.

The two-stage superefficient SBM model was chosen because it can (1) incorporate undesirable outputs such as CO₂ emissions, (2) account for input/output slacks, and (3) allow ranking of efficient DMUs. This study further extends this framework by adopting a non-oriented two-stage super-efficient network SBM model, whose core advantage lies in simultaneously optimizing input redundancy and output deficiency, including the non-expected output of CO₂ emissions. It does not require presupposing the direction of efficiency improvement and is more suitable for the complex input-output relationship in the two stages of production and operation in the aviation industry. However, its limitations include sensitivity to the choice of input–output indicators and the inability to fully capture external environmental shocks such as policy changes or market volatility.

Building on the heterogeneity among airlines in terms of scale, operational characteristics, and market environment, this study adopts a two-stage super-efficiency network SBM model with undesirable outputs under the variable returns to scale (VRS) assumption. Compared with the traditional radial DEA model, the SBM framework directly incorporates input slacks and output slacks into the objective function and is therefore more suitable for evaluating airline carbon emission efficiency, where both resource redundancy and output insufficiency may coexist. In addition, the network structure allows the internal production process of airlines to be decomposed into linked sub-stages rather than being treated as a “black box”.

Assume that there are n airlines, indexed by j = 1, 2, …, n, and each airline is regarded as a decision-making unit (DMU). The airline production system is divided into two connected stages:

Stage 1 (production stage): inputs are aviation fuel consumption and labor, and the desirable intermediate output is Available Seat Kilometers (ASK);

Stage 2 (operation stage): inputs are ASK and operational expenses (OPEX), desirable outputs are Revenue Passenger Kilometers (RPK) and operating revenue, and the undesirable output is CO₂ emissions.

For DMU j, denote:

• $x_{ij}^{(1)}\in R_{+}^{m_1}$: input vector of Stage 1,
• $z_{dj}\in R_{+}^q$: intermediate output vector of Stage 2,
• $x_{ij}^{(2)}\in R_{+}^{m_2}$: additional input vector of Stage 2,
• $y_{rj}^{(2)}\in R_{+}^s$: desirable output vector of Stage 2,
• $b_{lj}^{(2)}\in R_{+}^h$: undesirable output vector of Stage 2.

Let ${\lambda }_j^{(1)}$ and ${\lambda }_j^{(2)}$ be the intensity variables for the two stages. Under VRS, the production possibility sets of the two stages are defined as follows:

$$P^{(1)}=\left\{\left(x^{(1)},z\right):x^{(1)}\ge {\displaystyle \sum _{j=1}^n{\lambda }_j^{(1)}{x}_j^{(1)}},z\le {\displaystyle \sum _{j=1}^n{\lambda }_j^{(1)}{z}_j},{\displaystyle \sum _{j=1}^n{\lambda }_j^{(1)}}=1,{\lambda }_j^{(1)}\ge 0\right\}$$

(1)

$$P^{(2)}=\left\{\left(z,x^{(2)},y^{(2)},b^{(2)}\right):z\ge {\displaystyle \sum _{j=1}^n{\lambda }_j^{(2)}{z}_j},x^{(2)}\ge {\displaystyle \sum _{j=1}^n{\lambda }_j^{(2)}{x}_j^{(2)}},y^{(2)}\le {\displaystyle \sum _{j=1}^n{\lambda }_j^{(2)}{y}_j^{(2)}},b^{(2)}\ge {\displaystyle \sum _{j=1}^n{\lambda }_j^{(2)}{b}_j^{(2)}},{\displaystyle \sum _{j=1}^n{\lambda }_j^{(2)}}=1,{\lambda }_j^{(2)}\ge 0\right\}$$

(2)

For the evaluated DMU o, the non-oriented two-stage network SBM model is constructed as:

$$\min \rho ={\displaystyle \frac{{\displaystyle \sum _{k=1}^2{w}_k\left(1-\frac{1}{m_k}{\displaystyle \sum _{i=1}^{m_k}\frac{s_i^{k-}}{x_{io}^{\left(k\right)}}}\right)}}{{\displaystyle \sum _{k=1}^2{w}_k\left[1+\frac{1}{s_k}\left({\displaystyle \sum _{r=1}^{s_k}\frac{s_r^{k+}}{y_{ro}^{\left(k\right)}}}+{\displaystyle \sum _{l=1}^{h_k}\frac{s_l^{kb-}}{b_{lo}^{\left(k\right)}}}\right)\right]}}}$$

(3)

subject to

$$\begin{gathered} x_{io}^{\left(1\right)}={\displaystyle \sum _{j=1}^n{\lambda }_j^{\left(1\right)}{x}_{ij}^{\left(1\right)}}+s_i^{1-},\begin{array}{cc}& i=1,2,\dots ,m_1\end{array} \\ {z}_{do}={\displaystyle \sum _{j=1}^n{\lambda }_j^{\left(1\right)}{z}_{dj}-s_d^z},\begin{array}{cc}& d=1,2,\dots ,q\end{array} \\ {z}_{do}={\displaystyle \sum _{j=1}^n{\lambda }_j^{\left(2\right)}{z}_{dj}-s_d^{z^{\prime }}},\begin{array}{cc}& d=1,2,\dots ,q\end{array} \\ {x}_{io}^{\left(2\right)}={\displaystyle \sum _{j=1}^n{\lambda }_j^{\left(2\right)}{x}_{ij}^{\left(2\right)}+s_i^{2-}},\begin{array}{cc}& i=1,2,\dots ,m_2\end{array} \\ {y}_{ro}^{\left(2\right)}={\displaystyle \sum _{j=1}^n{\lambda }_j^{\left(2\right)}{y}_{rj}^{\left(2\right)}-s_i^{2+}},\begin{array}{cc}& r=1,2,\dots ,s\end{array} \\ {b}_{lo}^{\left(2\right)}={\displaystyle \sum _{j=1}^n{\lambda }_j^{\left(2\right)}{b}_{lj}^{\left(2\right)}+s_l^{2b-}},\begin{array}{cc}& l=1,2,\dots ,h\end{array} \\ {\displaystyle \sum _{j=1}^n{\lambda }_j^{\left(1\right)}}=1 \\ {\displaystyle \sum _{j=1}^n{\lambda }_j^{\left(2\right)}}=1 \\ {\lambda }_j^{\left(1\right)},{\lambda }_j^{\left(2\right)},s_i^{1-},s_i^{2-},s_r^{2+},s_l^{2b-}\ge 0 \end{gathered}$$

where ρ denotes the overall efficiency score; The term w_k in the objective function represents the stage weight assigned to the k-th sub-process in the network model. It reflects the relative importance of each stage. In line with Tone and Tsutsui (2009) [43] and Kao and Hwang (2008) [44], since the production stage and operation stage are equally critical for airline carbon emission efficiency, we set equal weights: w₁ = w₂ = 0.5. The equal weighting assumption (w₁ = w₂ = 0.5) implies that the model does not impose any ex-ante preference between production and operational stages, allowing efficiency contributions to be endogenously determined by slack structures. $s_i^{-}$ represents input redundancy, $s_r^{+}$ denotes desirable output shortfall, and $s_l^{b-}$ denotes undesirable output redundancy. A larger efficiency score indicates better overall performance. To further rank efficient DMUs, this study adopts the super-efficiency mechanism, under which the evaluated DMU is excluded from the reference set. Therefore, for DMU 0, the intensity variables are defined over $j\ne o$. The corresponding super-efficiency model can be written as:

$$\min {\rho }^{SE}$$

(4)

subject to the same constraints as above, but with

$${\displaystyle \sum _{j=1,j\ne o}^n{\lambda }_j^{\left(1\right)}}=1,{\displaystyle \sum _{j=1,j\ne o}^n{\lambda }_j^{\left(2\right)}}=1$$

(5)

This treatment enables efficient airlines to obtain scores greater than 1, thereby allowing a complete ranking of airlines. Overall, the two-stage super-efficiency network SBM model with undesirable outputs can simultaneously account for internal production structure, CO₂ emissions, and heterogeneity in airline scale, making it suitable for evaluating the static carbon emission efficiency of global airlines.

2.2.3. SBM-Based Hicks–Moorsteen Productivity Analysis Framework

The static two-stage SBM model evaluates carbon emission efficiency at a given point in time but does not capture intertemporal productivity changes. To analyze dynamic evolution, this study adopts the Hicks–Moorsteen (HM) productivity index based on non-oriented distance functions.

In this study, the HM index is computed at the system level using SBM distance functions defined over the overall production process. Let periods t and t + 1 denote two adjacent time periods. The HM productivity index is expressed as:

$$H{M}_o^{t,t+1}={\left[{\displaystyle \frac{D^t(X^{t+1},Y^{t+1},B^{t+1})}{D^t(X^t,Y^t,B^t)}}\times {\displaystyle \frac{D^{t+1}(X^{t+1},Y^{t+1},B^{t+1})}{D^{t+1}(X^t,Y^t,B^t)}}\right]}^{1/2}$$

(6)

where $D^t(\cdot )$ and $D^{t+1}(\cdot )$ are non-oriented SBM distance functions; X, Y, and B denote inputs, desirable outputs, and undesirable outputs. An HM value greater than 1 indicates productivity improvement.

For interpretative purposes only, we report two auxiliary indicators, efficiency change (EC) and technological change (TC). These formulations are adapted from single-stage DEA literature [45,46].

$$E{C}_o^{t,t+1}={\displaystyle \frac{D^t(X^{t+1},Y^{t+1},B^{t+1})}{D^t(X^t,Y^t,B^t)}}$$

(7)

$$T{C}_o^{t,t+1}=\sqrt{{\displaystyle \frac{D^t(X^{t+1},Y^{t+1},B^{t+1})}{D^{t+1}(X^{t+1},Y^{t+1},B^{t+1})}}\times {\displaystyle \frac{D^t(X^t,Y^t,B^t)}{D^{t+1}(X^t,Y^t,B^t)}}}$$

(8)

Note: The theoretical foundations of the HM index and its decomposition were developed for single-stage DEA models and do not strictly apply to two-stage network structures. Multiplicative separability does not hold in our two-stage SBM framework. Therefore, EC and TC are solely interpretative and heuristic tools to support intuitive economic discussion. They do not constitute a mathematically rigorous decomposition of the HM index for the network model.

2.3. Description of the Data

This study selects data from 2015 to 2021, with the core reason being that this period was a critical turning point for global aviation industry carbon reduction policies and actual operations. On the one hand, 2015 marked the United Nations Climate Change Conference (COP21), which established the global carbon neutrality target, and the period from 2020 to 2021 covered the full impact of the COVID-19 pandemic on the aviation industry and its initial recovery, forming a complete cycle of “policy launch–steady growth–crisis impact–recovery emergence”, providing an ideal scenario for analyzing efficiency volatility and recovery patterns. On the other hand, this unique time window can accurately capture the evolution law of carbon efficiency driven by external shocks (the pandemic) and policies, providing more valuable empirical evidence for the sustainable development of the aviation industry in the post-pandemic era. In contrast, simply pursuing the latest data (such as from 2022 to 2023) can only reflect the single state after recovery and cannot reveal the efficiency fluctuation mechanism and convergence trend before and after the crisis.

Based on data accessibility criteria, we selected 18 representative airlines for our sample, with regional distribution as follows: 5 in Europe, 4 in North America, 8 in Asia, and 1 in Oceania. The limited representation from Oceania (only one airline) stems from most carriers in the region not disclosing sustainability reports during 2015–2021, making key carbon efficiency metrics—such as aviation kerosene consumption and greenhouse gas emissions—unavailable for measurement. Specifically, three major carriers in Oceania, namely Virgin Australia, Jetstar Airways and Regional Express Aviation (see

Table 3. Missing data.

Geographic Location	Major Civil Aviation Enterprises	Missing Data	Missing Year
Oceania	Virgin Australia	AF, CEs	All years
	Jetstar Airways	AF, CEs	All years
	Regional Express Aviation	AF, CEs	All years

for details), were excluded from the final sample, as they failed to disclose key indicators like aviation fuel consumption and CO₂ emissions in their sustainability reports throughout 2015–2021. While this sample exhibits regional asymmetry, it ensures measurement accuracy and intertemporal comparability, offering empirical value.

The data for AF, ASK, NE, OPEX, RPK, and R were obtained from the annual reports and financial statements of the respective airlines, while the data for CO₂ emissions were collected from corporate sustainability reports and environmental disclosures. When necessary, supplementary information was cross-checked with ICAO, IATA, and publicly available aviation statistics databases.

Table 4. Basic information about the selected airline.

Airlines	IATA Code	Country	Area
Lufthansa	LH	Germany	Europe
Scandinavian Airlines	SK	Sweden, Denmark, Norway
British Airways	BA	United Kingdom
Norwegian Air Shuttle	DY	Norway
Finnair	AY	Finland
Delta Air Lines	DL	United States	North America
United Airlines	UA	United States
American Airlines	AA	United States
Southwest Airlines	WN	United States
Air China	CA	China	Asia
China Eastern Airlines	MU	China
China Southern Airlines	CZ	China
Hainan Airlines	HU	China
Cathay Pacific Airways	CX	China
Singapore Airlines	SQ	Singapore
All Nippon Airways	NH	Japan
Emirates	EK	United Arab Emirates
Qantas	QF	Australia	Oceania

shows the country, IATA code and geographic location of these 18 airlines. These airlines represent the diversity of different regions, and their diverse characteristics in terms of size, country and business model provide favorable conditions for an in-depth study of the carbon emission efficiency of different types and sizes of airlines.

Its basic data include information on AF, NE, ASK, OPEX, RPK, CEs, and R of the selected airline companies in 2015–2021. The data for AF, ASK, NE, OPEX, RPK, and R are obtained from the annual reports of various airlines, while the CEs data specifically comes from the sustainability reports and corporate social responsibility reports of the sample airlines.

Table 5. Descriptive statistics of inputs and outputs, 2015–2021.

Indicators	Minimum	Maximum	Mean	Std. Dev.
Aviation fuel (AF, kiloton)	365.49	15,925.22	5980.86	4119.92
Number of employees (NE)	4906.00	137,784.00	54,288.65	40,845.49
Operational expenses (OPEX)	51.00	964.00	463.57	290.37
Revenue passenger kilometers (RPK, million)	2890.60	299,967.00	127,280.97	83,392.32
Operating income (R, million USD)	542.28	47,007.00	16,367.44	11,648.22
Carbon dioxide emissions (CEs, million tons)	23.88	4206.79	1716.41	1122.87
Available seat kilometers (ASK, million)	7687.70	390,775.00	161,004.05	98,464.79

shows the descriptive statistical analysis of the data of the 18 airline companies for the years 2015–2021.

Table 6. Input-output Spearman correlation.

	ASK	RPK	R	CEs
AF	0.831 **
NE	0.785 **
ASK		0.920 **	0.821 **	0.892 **
OPEX		0.605 **	0.736 **	0.755 **

Note: ** indicates a significant correlation at the 0.01 level (two-tailed).

shows that the Spearman correlation coefficients for all input and output indicators are greater than 0.6, indicating a very strong relationship between the input and output indicators. All correlation coefficients are significant.

Figure 2 illustrates that the total carbon emissions of these 18 airlines increased from 31.332 million tons in 2015 to 37.620 million tons in 2019, with an average annual growth rate of 4.32%. This growth is attributed to economic globalization, which drove increased travel demand and, consequently, expanded global air traffic volume [47]. Until 2020, carbon emissions decreased to 18.232 million tons due to the epidemic. The annual trends of RPK and CEs of the selected carriers in this paper are similar from 2015–2021, rising in 2015–2019, falling sharply in 2020 and recovering slightly in 2021. Carbon emission intensity (CEs/RPK) fluctuates between 12–13 in 2015–2019 and rises steeply to 17.8 in 2020 due to the impact of the epidemic, which has seen the RPK value fall far more than carbon emissions, and an IATA report shows that the global aviation industry expects the RPK to remain at 40% of its precrisis level by 2021 [48].

Figure 3 shows the cumulative change in carbon emissions of these 18 carriers from 2015–2021. Most of these airline companies’ carbon emissions show a wavy line trend of first increasing, then decreasing and then increasing. Among the airlines, the changes in HU are the most obvious, which may be due to HU’s acquisitions and mergers of airlines such as Xinhua Airlines and Shanxi Airlines in 2017, resulting in a significant expansion of HU’s transportation scale after that [49]. In 2015–2018, CEs rose sharply as airlines expanded rapidly in size and air transportation; in 2018–2020, CEs decreased rapidly as airlines operated in dismal conditions due to the outbreak, and many aircraft of civil aviation companies were grounded; in 2021, CEs rose as the global aviation industry recovered from the COVID-19 pandemic [50]. SK, CX, LH, LH, DY, AY, and SQ’s CEs in 2019–2020 is even less than half of what it was in 2015, suggesting that the operating conditions of these companies have been severely affected by the epidemic; DY, SK, and CX’s CEs in 2020–2021 are still persistently low, suggesting that these three airlines will not be able to easily return to normalcy from the global aviation depression caused by pandemic operations.

It should be emphasized that this study focuses on structural dynamics and efficiency evolution under external shocks, rather than providing a real-time assessment of current airline performance. Therefore, the findings should be interpreted as structural insights rather than contemporaneous performance evaluations.

3. Results

3.1. Static Carbon Efficiency of Airlines

3.1.1. Overall Pattern

To clarify the interpretation of efficiency values presented in this section, the efficiency value under the non-oriented model reflects an airline’s comprehensive potential to optimize both input factors such as fuel consumption and labor force, and expected outputs like Available Seat Kilometers (ASK) and operating revenue (R), while minimizing undesirable outputs such as CO₂ emissions, all within its existing technological and resource constraints. Efficiency decomposition under the VRS assumption reveals that the low efficiency of some airlines, such as AA and WN, primarily stems from insufficient pure technical efficiency rather than scale inefficiency. This finding provides a basis for subsequent differentiated policy recommendations. The static carbon efficiency of the 18 airlines studied from 2015 to 2021 exhibited significant fluctuations (see Figure 4). Among these carriers, SQ, UA, HU, and DY experienced the most substantial changes in overall efficiency. Between 2015 and 2019, most airlines (especially SQ, AY and EK) demonstrated stable and relatively high static carbon efficiency. However, the outbreak of the pandemic in 2020 led to a sharp decline in global air travel demand, causing a widespread decrease in carbon efficiency, particularly in the operational and production stages.

Table 7. Overall efficiency of the airline companies in 2015–2021.

Airline	2015	2016	2017	2018	2019	2020	2021	Mean	Rank
AA	0.280	0.224	0.229	0.240	0.248	0.149	0.204	0.2249	18
AY	0.683	0.705	0.801	0.806	0.814	0.670	0.127	0.6579	2
BA	0.542	0.475	0.485	0.483	0.534	0.199	0.206	0.4177	9
CA	0.354	0.362	0.373	0.405	0.410	0.212	0.208	0.3320	13
CX	0.604	0.522	0.525	0.570	0.549	0.198	0.078	0.4354	8
CZ	0.312	0.339	0.354	0.386	0.398	0.243	0.250	0.3259	15
DL	0.419	0.397	0.408	0.446	0.488	0.198	0.312	0.3810	12
DY	0.534	0.572	0.631	0.742	0.769	0.168	0.144	0.5083	6
EK	0.667	0.681	0.710	0.721	0.715	0.205	0.476	0.5964	4
HU	0.549	0.540	0.557	0.141	0.168	0.054	0.062	0.2959	16
LH	0.565	0.545	0.573	0.582	0.564	0.237	0.315	0.4828	7
MU	0.333	0.343	0.436	0.383	0.382	0.261	0.167	0.3293	14
NH	0.655	0.723	0.679	0.732	0.740	0.599	0.352	0.6399	3
QF	0.430	0.421	0.448	0.544	0.451	0.325	0.178	0.3996	11
SK	0.435	0.425	0.472	0.478	0.473	0.301	0.247	0.4045	10
SQ	0.932	0.816	0.879	0.823	0.805	0.066	0.313	0.6619	1
UA	0.900	0.882	0.479	0.509	0.515	0.190	0.319	0.5421	5
WN	0.307	0.304	0.318	0.316	0.320	0.154	0.255	0.2819	17

shows the changes in static carbon efficiency among the airlines, indicating that most airlines performed well in the years before the pandemic (2015–2019), especially SQ and AY, whose production and operational efficiencies remained high across nearly all years. In 2020, as the global aviation industry plunged into a downturn, nearly all airlines experienced a significant decline in efficiency, reflecting the immense challenges faced by airlines in dealing with large-scale flight cancellations, reduced flight numbers, and a sharp decrease in passenger traffic. In 2021,

Table 8. Airline stage efficiency in 2015–2021.

Year	2015		2016		2017		2018		2019		2020		2021		Rank
Airlines	Stage 1	Stage 2	Stage 1	Stage 2	Stage 1	Stage 2	Stage 1	Stage 2	Stage 1	Stage 2	Stage 1	Stage 2	Stage 1	Stage 2	Stage 1	Stage 2
AA	0.323	0.610	0.264	0.560	0.265	0.571	0.265	0.588	0.264	0.599	0.196	0.497	0.218	0.566	17	17
AY	0.579	0.887	0.598	0.898	0.602	1.000	0.612	1.000	0.627	1.000	0.340	1.000	0.193	0.448	5	1
BA	0.411	0.836	0.423	0.763	0.427	0.772	0.439	0.764	0.457	0.805	0.280	0.518	0.282	0.512	11	9
CA	0.402	0.652	0.414	0.648	0.425	0.649	0.439	0.683	0.459	0.663	0.311	0.527	0.301	0.537	10	13
CX	0.209	1.000	0.437	0.791	0.447	0.791	0.454	0.843	0.466	0.812	0.196	0.456	0.092	0.198	15	10
CZ	0.434	0.565	0.400	0.623	0.415	0.625	0.439	0.652	0.461	0.643	0.351	0.538	0.342	0.575	8	15
DL	0.255	0.755	0.258	0.731	0.256	0.743	0.260	0.798	0.265	0.855	0.233	0.518	0.253	0.640	18	6
DY	0.564	0.720	0.661	0.712	0.791	0.709	1.000	0.742	0.985	0.775	0.227	0.502	0.119	0.529	2	11
EK	0.427	0.952	0.431	0.956	0.437	0.988	0.441	1.000	0.430	1.000	0.163	0.465	0.292	0.792	12	2
HU	0.657	0.692	0.631	0.689	0.808	0.633	0.742	0.175	0.789	0.195	0.051	0.258	0.051	0.256	4	18
LH	0.341	0.895	0.349	0.870	0.373	0.886	0.383	0.890	0.385	0.871	0.230	0.550	0.280	0.608	14	4
MU	0.381	0.643	0.397	0.634	0.427	0.678	0.445	0.650	0.461	0.628	0.328	0.525	0.326	0.405	9	16
NH	0.388	0.736	0.347	0.748	0.372	0.762	0.431	0.829	0.371	0.764	0.263	0.694	0.173	0.500	13	7
QF	0.567	0.868	0.566	0.940	0.635	0.862	0.625	0.901	0.628	0.926	0.198	1.000	0.521	0.571	3	3
SK	0.459	0.705	0.507	0.672	0.524	0.711	0.537	0.709	0.537	0.704	0.457	0.508	0.481	0.429	6	12
SQ	0.863	1.000	0.846	0.889	0.844	0.955	1.000	0.823	1.000	0.805	0.339	0.147	0.681	0.412	1	8
UA	1.000	0.900	1.000	0.882	0.263	0.819	0.299	0.835	0.030	1.000	0.236	0.478	0.272	0.634	7	5
WN	0.279	0.650	0.278	0.648	0.279	0.663	0.281	0.663	0.275	0.668	0.257	0.450	0.277	0.596	16	14

shows as the aviation industry gradually recovered, some airlines (such as EK and SQ) swiftly regained their efficiency levels, demonstrating their strong recovery capability. This is due to SQ’s improvement measures in the production phase: the introduction of the Airbus A350-900 in 2015, which has higher fuel efficiency and lower carbon emissions, and the use of renewable synthetic fuels in aircraft in 2021 [51]. High-efficiency airlines have implemented targeted measures in both the production and operational stages. For example, AY—ranked second in overall efficiency—has introduced the Boeing 787-9 Dreamliner, the Airbus A321neo LR and the Boeing 737 MAX 10 at the production stage, all of these aircraft models improve fuel efficiency. On the operational side, they launched Norwegian Reward, their first global loyalty program, in 2016, which provides passengers with additional benefits and rewards, such as free airfare, free baggage, and free airport lounges, which both increase attendance and reduce carbon emissions per passenger [52]. NH, ranked third, will combine four strategic approaches to improve production, operations, and carbon efficiency: aircraft operational improvements and technological innovations, use of sustainable aviation fuels, carbon trading, and negative emission technologies [53]. In the future, other inefficient airlines, such as AA, WN, and HU, may adopt similar improvements.

Overall, the fluctuations in the carbon efficiency of airlines are closely linked to the overall development of the international aviation industry, influenced by factors such as the macroeconomic environment, aviation policies, and global health crises.

3.1.2. Phased Analysis

A further analysis of the efficiency differences among airlines in the production and operation stages reveals significant disparities in carbon efficiency performance between these two stages. Table 8 shows that NH performs well in both the production and operation stages, ranking 3rd in both stages, and its operation efficiency in 2020 reaches 1, which indicates that its operation has recovered well after the outbreak. AY’s efficiency in the production stage is only ranked 5th, but its efficiency in the operation phase was ranked 1st almost every year, in which it reached 1 in 2017, 2018, 2019, and 2020, so if AY wants to continue to improve its carbon emission performance and airline efficiency, it should start from improving its energy use efficiency and enhancing its transportation capacity. Of all the airlines, EK has the most significant differences in production and operational efficiency. Despite being ranked 12th in terms of efficiency in the production phase, it is second highest in terms of operational efficiency. This advantage is due to its continuous service quality improvements, such as the “Home Check-In” policy introduced in 2018, which offers customers the convenience of checking in their luggage online and staff picking up their luggage from their hotels or homes [54]. These measures have enhanced EK’s customer stickiness and airplane attendance.

Notably, large U.S. airlines, e.g., DL, AA, and WN, are generally inefficient in the production phase, while Chinese airlines, e.g., HU, MU, and CZ, are generally inefficient in the operational phase. This suggests that U.S. airlines need to focus more on technological innovation to improve production efficiency. Chinese airlines, on the other hand, should focus more on improving their operations to further optimize and enhance their operational performance.

In addition, the average operational efficiency of airlines is generally higher than the average production efficiency, which is found in 16 airlines: AA, AY, BA, CA, CX, CZ, DL, DY, EK, LH, MU, NH, QF, SK, UA, and WN. Among them, SQ’s two-stage efficiency is higher than 0.7, and the gap between the two-stage efficiency is smaller compared to other airlines. AY, EK, and QF’s average operational efficiency is higher than 0.8, but the gap with production efficiency is very large, among which the difference between EK’s production efficiency and operational efficiency is 0.5. Therefore, for most civil aviation companies, especially EK, to improve carbon emission efficiency, it is necessary to improve energy efficiency from the beginning, such as procuring the latest generation of airplanes with advanced fuel efficiency, and incorporating sustainable, clean energy sources into operations. The results are shown in Figure 5.

3.1.3. Regional Disparities

To study the geographic variability of airlines’ overall efficiency and two-stage efficiency, the airlines are categorized by continent (a total of four), and radar charts are made, as shown in Figure 6. The airlines in Europe have higher overall efficiency and operational efficiency than those of the other three continents because most of the European airlines have higher efficiency, e.g., AY and DY. The Asian airlines have slightly lower overall efficiency than European carriers but higher production efficiency than American airlines; for example, the production efficiency is higher than that of American airlines because EK and NH have an operational efficiency higher than 0.86, as shown in Table 8. The lower overall efficiency of the American airlines is due to low productivity, with an overall average of 0.307, which is lower than that of the other three continents.

3.1.4. Convergence Trends

To characterize the different evolutions of airline efficiency at different stages, an absolute β-convergence analysis was performed on the total-stage efficiency, the first-stage efficiency, and the second-stage efficiency of 18 airlines around the world [47]. Absolute β-convergence means that an airline’s total stage efficiency or substage efficiency will converge to the same level of steady-state growth. β-convergence can be obtained from the following regression analysis model:

$$\ln (y_{it}/y_{i0})=\alpha +\beta \ln (y_{i0})+{\epsilon }_{it}$$

(9)

y_i0, y_it is the efficiency value of the ith carrier in period 0 and period t, ln(y_it/y_i0) denotes the rate of change in the efficiency of the ith carrier from period 0 to period t, α is the constant of the intercept term, which denotes the efficiency level representing the initial period 0, β is the coefficient of the logarithmic value of the efficiency value of the carrier in the base period, which denotes the effect of the change in the efficiency of the carrier in the efficiency level of period 0 on the rate of growth of the efficiency; and ε_it denotes the random perturbation term. When β < 0 and is significant, it indicates that there is absolute convergence in the value of carrier efficiency. The Hausman test was utilized to examine the airline panel data, and the results showed that the fixed effects regression model was more appropriate [55]. The results are shown in

Table 9. The result of absolute convergence of airline efficiency.

Stage	Variables	All Samples
Overall stage	β	−0.4123895 ***
	α	0.2938045 ***
	R2	0.128
	F-stata	13.07
Production stage	β	−0.5076467 ***
	α	0.4514505 ***
	R2	0.1791
	F-stata	19.42
Operation stage	β	−0.5117273 ***
	α	0.4241398 ***
	R2	0.1873
	F-stata	20.52

Note: *** denotes the 1% significance level.

.

The regression coefficients of the total stage and substage are both negative and pass the significance test of 1%, which indicates that there is absolute β-convergence in the efficiency of these 18 airlines; i.e., the gap between the overall efficiency of the airlines and the efficiency of the airlines in the substage is gradually decreasing, and there is a catching-up effect of the inefficient airlines to the efficient airlines. The regression coefficient β indicates that the convergence of efficiency in the operation stage is faster than that in the production stage; i.e., for airlines with lower static carbon emission efficiency (AA, WN, HU, etc.), the efficiency in the operation stage has a greater possibility of catching up with that of the high-efficiency airlines, whereas that in the production stage is slightly more difficult.

The R² values reported in Table 9 range from 0.128 to 0.1873. Although these values may appear relatively modest, such magnitudes are common in efficiency convergence studies using cross-sectional panel data, where efficiency dynamics are influenced by multiple external factors (e.g., market conditions, technological changes, and policy environments) that are not fully captured in the regression model.

Therefore, the estimated models still provide meaningful explanatory power for identifying β-convergence trends in airline carbon emission efficiency. Similar levels of explanatory power have also been reported in previous DEA-based convergence studies.

Overall, although there are significant differences in static carbon efficiency across the global aviation industry, low-efficiency airlines are steadily narrowing the gap with high-efficiency airlines as technology advances and management practices improve. This trend indicates that policy support and market incentives play a crucial role in enhancing overall industry efficiency.

3.2. Dynamic Carbon Efficiency of Airlines

3.2.1. HM Index Trends

The dynamic changes in carbon efficiency are evaluated using the SBM-based Hicks–Moorsteen (HM) productivity index, which measures overall productivity variations over time. As noted in the methodology, EC and TC are used only for interpretative and heuristic purposes, not as a strict decomposition. As shown in

Table 10. Super-Efficiency SBM-based Hicks–Moorsteen (HM) index for 18 airlines, 2015–2021.

HM	15/16	16/17	17/18	18/19	19/20	20/21	Mean	Rank
AA	1.000	1.008	1.028	1.014	0.576	1.492	1.020	5
AY	1.043	0.992	1.020	0.999	0.277	1.546	0.979	9
BA	0.938	1.022	1.016	1.074	0.449	0.982	0.914	13
CA	1.012	0.997	1.069	0.965	0.651	0.985	0.946	12
CX	0.997	1.027	1.023	0.991	0.399	0.590	0.838	18
CZ	1.025	1.030	1.045	1.010	0.730	1.046	0.981	8
DL	0.981	1.009	0.998	0.997	0.499	1.709	1.032	3
DY	1.830	1.213	1.262	0.996	0.201	0.668	1.028	4
EK	1.091	1.022	1.033	0.946	0.293	1.894	1.047	1
HU	0.992	1.586	0.486	1.114	0.412	1.153	0.957	10
LH	0.987	1.010	1.020	1.001	0.553	1.164	0.956	11
MU	1.010	1.066	0.992	0.977	0.799	0.521	0.894	15
NH	1.157	0.967	0.981	1.048	0.753	1.036	0.991	7
QF	1.001	1.012	0.959	1.067	0.899	0.360	0.883	16
SK	1.051	1.082	1.039	0.958	0.700	0.649	0.913	14
SQ	0.901	1.019	0.952	0.972	0.194	2.230	1.045	2
UA	0.942	0.278	1.072	0.998	0.511	1.458	0.877	17
WN	0.988	1.010	0.984	0.985	0.564	1.520	1.009	6
Mean	1.053	1.020	0.999	1.006	0.526	1.167	0.962

, the mean value of the HM index of EK, SQ, DL, DY, AA, and WN in 2015–2021 is greater than 1, and the dynamic carbon emission efficiency of these six airlines increases during the study period, while the other airlines decrease overall. The interpretative evidence suggests that the HM index of all 18 airlines shows a decline in 2019–2020 and has a mean value of 0.526, mainly due to the enormous impact of the COVID-19 pandemic on the world’s aviation industry, with a 50% decline in the world’s flight seat capacity and a 60% decline in the total number of passengers in 2020 [52]. After the outbreak, SQ, EK, DL, AY, AA, UA, and NH recovered better overall, with their HM index exceeding 1.4. CX, DY, MU, QF, and SK still need more time to recover, which is consistent with the data description in Section 2.3. The mean HM index was close to or above 1 in most adjacent periods, except for 2017–2018, when it was slightly below 1, and 2019–2020, when it declined sharply to 0.526 due to the pandemic shock. This is mainly because HU’s carbon emission performance declined too fast during this period, which may be due to the decline in management efficiency caused by the sudden expansion of the company’s size after HU’s acquisitions and mergers of Xinhua Airlines, Shanxi Airlines and other airlines in 2017, as mentioned in the previous section.

3.2.2. Interpretative Analysis Using EC and TC Indicators (Heuristic Only)

To support intuitive interpretation of productivity dynamics, we report EC and TC as heuristic indicators, not as a strict decomposition. As emphasized in the methodology section, these indicators are used for qualitative discussion only and do not represent a formal decomposition under the two-stage network structure. Although EC and TC are reported for interpretative purposes, they should not be understood as a strict decomposition of the HM index in a two-stage network framework.

The HM index is further interpreted using two auxiliary indicators, namely efficiency change (EC) and technological change (TC), to provide intuitive insights into productivity dynamics, with results presented in

Table 11. EC Index for 18 airlines, 2015–2021.

EC	15/16	16/17	17/18	18/19	19/20	20/21	Mean	Rank
AA	1.129	0.979	1.036	1.053	1.706	1.047	1.158	3
AY	1.091	1.050	0.955	1.044	0.852	1.068	1.010	14
BA	1.107	1.000	1.014	1.127	1.223	0.657	1.021	13
CA	1.139	0.973	1.074	1.000	1.944	0.649	1.130	5
CX	1.429	1.013	1.017	1.002	1.028	0.248	0.956	18
CZ	1.142	1.003	1.053	1.047	2.178	1.072	1.249	1
DL	1.079	0.985	0.995	1.039	1.374	1.401	1.146	4
DY	1.865	1.076	1.124	0.985	0.365	0.558	0.996	15
EK	1.189	1.006	1.012	0.983	0.890	1.322	1.067	11
HU	0.601	1.676	0.174	1.101	2.033	0.643	1.038	12
LH	1.146	0.993	1.017	1.035	2.024	0.563	1.130	6
MU	1.135	1.039	0.999	1.013	2.599	0.433	1.203	2
NH	1.335	1.216	0.944	1.016	1.097	0.982	1.098	10
QF	1.134	0.994	0.944	1.116	2.307	0.274	1.128	9
SK	1.125	1.063	1.034	1.001	2.036	0.516	1.129	7
SQ	0.963	1.009	0.919	0.976	0.877	1.038	0.964	17
UA	0.909	0.278	1.074	1.093	1.476	1.129	0.993	16
WN	1.051	0.987	0.977	1.021	1.646	1.089	1.128	8
Mean	1.143	1.019	0.965	1.036	1.536	0.816	1.086

and

Table 12. TC Index for 18 airlines, 2015–2021.

TC	15/16	16/17	17/18	18/19	19/20	20/21	Mean	Rank
AA	0.886	1.029	0.993	0.963	0.338	1.424	0.939	11
AY	0.956	0.945	1.067	0.957	0.326	1.447	0.950	7
BA	0.848	1.022	1.002	0.953	0.367	1.496	0.948	8
CA	0.889	1.026	0.995	0.965	0.335	1.517	0.954	6
CX	0.698	1.014	1.006	0.989	0.388	2.378	1.079	2
CZ	0.898	1.027	0.993	0.964	0.335	0.976	0.865	18
DL	0.909	1.025	1.003	0.959	0.363	1.220	0.913	15
DY	0.981	1.128	1.123	1.011	0.550	1.197	0.998	5
EK	0.918	1.016	1.021	0.962	0.329	1.433	0.946	9
HU	1.650	0.946	2.787	1.012	0.203	1.794	1.399	1
LH	0.862	1.018	1.003	0.967	0.273	2.070	1.032	4
MU	0.890	1.027	0.993	0.964	0.307	1.203	0.897	17
NH	0.867	0.796	1.040	1.032	0.686	1.054	0.912	16
QF	0.882	1.018	1.017	0.956	0.390	1.315	0.930	13
SK	0.934	1.018	1.004	0.958	0.344	1.259	0.920	14
SQ	0.935	1.010	1.035	0.995	0.221	2.148	1.058	3
UA	1.037	1.001	0.998	0.914	0.346	1.292	0.931	12
WN	0.940	1.024	1.007	0.965	0.343	1.395	0.946	10
Rank	0.943	1.005	1.116	0.972	0.358	1.479	0.979

. Except for CX, DY, SQ, and UA, all other airlines have an average EC index greater than 1 during the study period; i.e., the average managerial efficiency is improved during 2015–2021. Among them, CZ and MU are the most obvious, which are all Chinese airlines. The EC index of CX and DY is less than 1 because the EC index in 2020–2021 is too low, at 0.248 and 0.558, respectively, which indicates that the recovery of the company’s operation status after the epidemic is not good, and the EC index of SQ in 2018–2019 is too low (only 0.87); that is, it is too seriously affected by the epidemic. SQ’s management efficiency is far from the pre-2019 level, although the EC index rises to 1.129 in 2020–2021, and UA’s EC index is only 0.278 in 2016–2017.

From Table 12, the following conclusion can be drawn: HU ranked first in the average TC index, showing the best performance in terms of technological progress during the study period. It is noteworthy that especially in 2017–2018, its TC index is as high as 2.787, which indicates that HU has achieved significant improvement in terms of technological advancement despite a more severe decline in management efficiency. Next in line are CX and SQ, which are also Asian carriers. Although their TC indices may not be as good as HUs, they have also made considerable progress in terms of technological advancement. However, the worst performers are CZ and MU at 0.86 and 0.89, respectively, which are also Asian airlines but show an overall decline in technology levels. This may reflect the fact that large airlines may need more time and resources to make technology upgrades and improvements to meet evolving market demands.

To study the causes of the decline in the dynamic productivity change of airlines’ carbon emissions more clearly, the HM index of all airlines during the study period was classified according to Table 11, and the years with HM less than 1 were selected and analyzed for the causes of the decline in the HM index according to Table 11 and Table 12, and the results are shown in

Table 13. Summary of the interpretative analysis of dynamic productivity changes in airline carbon emissions.

Airlines	HM < 1	EC < 1	TC < 1	Main Cause
AA	1	1	4	TC
AY	3	2	4	TC
BA	3	2	3	TC
CA	4	3	4	TC
CX	4	1	3	TC
CZ	1	0	5	TC
DL	4	2	3	TC
DY	3	3	2	TC
EK	2	2	3	EC, TC
HU	3	3	2	EC
LH	2	2	3	TC
MU	4	2	4	TC
NH	3	2	3	TC
QF	3	3	3	EC
SK	3	1	3	TC
SQ	4	4	3	EC, TC
UA	4	2	3	EC, TC
WN	4	2	2	TC

. The causes of airlines’ dynamic carbon efficiency decline can be categorized into three groups. First, there is a group of dynamics, such as AA, AY, BA, CA, CX, CZ, DL, DY, LH, MU, NH, SK, and WN, whose HM index declines are mainly due to insufficient technological progress. Second, HU and QF, whose HM index decreases are mainly due to decreasing managerial efficiency. Finally, we have EK, SQ, and UA, whose HM index declines is limited both by insufficient technological progress and decreasing managerial efficiency.

3.2.3. Regional Comparisons

Figure 7 and Figure 8 show the changes in the dynamic carbon emission efficiency of airlines on four continents from 2015–2021. The trend of dynamic carbon emission efficiency changes of airlines on the four continents during the study period is basically the same, except that the airlines in Australia (QF) still show a decreasing trend during 2020–2021, which is due to the EC index being too low during this period, only 0.273, which indicates that QF has not recovered well after the epidemic. The dynamic carbon efficiency of European airlines was slightly higher than that of carriers from the other three continents until 2019, but European carriers were more severely hit than those from the other three continents during the epidemic and recovered the slowest, while Asian carriers were relatively less hit and recovered the fastest. The main reason for this is that Asian carriers have higher EC indices than European carriers in 2019–2020 and 2020–2021 and higher TC indices than the other three continental carriers in 2020–2021. In addition, airlines on all four continents had EC indices above 1 and TC indices below 1 in 2019–2020; i.e., the management efficiency of airlines on all four continents increased during the COVID-19 pandemic, while the overall technical level declined.

3.2.4. Convergence Analysis

Absolute β-convergence analysis was conducted on the HM index and its heuristic auxiliary indicators EC and TC to examine whether these indicators converge toward a steady-state level across airlines. The attainment of β-convergence can still be derived from Equation (10) above.

Table 14. Results of absolute β-convergence for the HM index and auxiliary EC/TC indicators.

Index	Variables	All Samples
HM	β	−1.697682 ***
	α	1.537923 ***
	R2	0.6479
	F-stata	130.67
EC	β	−1.480456 ***
	α	1.492364 ***
	R2	0.7019
	F-stata	167.16
TC	β	−1.918828 ***
	α	1.931601 ***
	R2	0.7219
	F-stata	184.35

Note: *** denotes the 1% significance level.

demonstrates that the regression coefficients (β) for the HM, EC, and TC indices of all airlines consistently exhibit negative values, passing significance tests at the 1% level. This signifies the existence of absolute β-convergence in the dynamic carbon emission efficiency and its auxiliary indices across the selected airlines. Airlines with lower dynamic carbon emission efficiency showcase a superior rate of improvement compared to those with higher efficiency. The β coefficients further indicate that the convergence speed and homogeneity of the TC index among airlines are faster than those of the EC index. In essence, airlines with lower dynamic carbon emission efficiency are more likely to catch up with their more efficient counterparts in terms of technological efficiency.

3.3. Policy Implications

The carbon emission efficiency performance of airlines is influenced by a variety of internal and external factors. Based on the empirical analysis of 18 airlines from 2015 to 2021, this study identifies four major determinants of carbon efficiency: technological advancement, management efficiency, policy environment, and market factors. These factors jointly shape the evolution of both static and dynamic carbon efficiency in the global aviation industry.

3.3.1. Short-Term Measures: Enhancing Operational Efficiency

Most airlines demonstrate higher operational efficiency than production efficiency, indicating that management and operational improvements can deliver relatively quick carbon reduction benefits. Managerial efficiency plays an equally important role in shaping carbon efficiency outcomes. Effective management allows airlines to optimize operational processes, reduce unnecessary fuel consumption, and improve resource utilization. For instance, EK has implemented advanced flight scheduling systems that minimize idle flight time and route overlap, thereby reducing energy use and emissions. AY has adopted data-driven management practices to increase aircraft utilization rates and streamline service operations, contributing indirectly to higher carbon efficiency. Hence, airlines should prioritize optimizing flight routes, improving load factors, and adopting digital management platforms for predictive maintenance and real-time scheduling. Such measures are cost-effective, scalable, and can be implemented immediately across the industry. Specific recommendations include:

(1)

Optimization of Flight Scheduling and Route Networks

Governments and regulatory bodies should provide data support and operational incentives to encourage airlines to redesign flight schedules and optimize route networks. Advanced scheduling systems and air traffic management technologies can reduce fuel burn and turnaround time, enhancing both economic and environmental performance.

(2)

Digitalization and Intelligent Operations

Policymakers should encourage airlines to invest in digital management systems—such as predictive maintenance, real-time dispatch, and energy monitoring platforms—to improve operational efficiency and minimize unnecessary emissions.

(3)

Mandatory Carbon Reporting and Transparency

Governments can introduce mandatory carbon reporting frameworks requiring airlines to disclose emissions data regularly. Enhanced transparency will not only facilitate benchmarking but also create incentives for airlines to adopt cleaner operational practices through public accountability and recognition.

3.3.2. Medium-Term Strategies: Promoting Technological Innovation

Market conditions also play a crucial role in influencing airlines’ carbon efficiency. Fluctuations in fuel prices, market demand, and competitive pressures directly affect operational and environmental performance. During 2015–2018, when oil prices were relatively low, many airlines increased flight frequency and passenger capacity, thereby improving efficiency through economies of scale. However, the rise in fuel prices in 2019 increased cost pressures and prompted airlines to pursue operational optimization, including more efficient scheduling and energy management systems. Market competition likewise incentivizes airlines to enhance carbon efficiency. In highly competitive markets, carriers are compelled to reduce operational costs and improve environmental performance to attract environmentally conscious passengers. For example, European airlines’ superior performance in carbon efficiency is partially attributable to market-driven pressure to align with consumer expectations for greener air travel.

The policy environment exerts a profound influence on airlines’ carbon efficiency performance. Environmental regulations, carbon trading mechanisms, and government-led sustainability initiatives directly affect airlines’ decarbonization strategies. Market-based instruments, including participation in carbon offsetting and trading schemes such as ICAO’s CORSIA and regional initiatives like the EU Emissions Trading Scheme, can provide transitional solutions for emission mitigation. Policymakers should strengthen regulatory frameworks to ensure the credibility and liquidity of carbon markets while encouraging greater transparency in emission disclosures. For example, SQ has responded proactively to global environmental regulations by implementing comprehensive sustainability programs, including carbon offsetting schemes, green fleet procurement, and fuel-saving initiatives. These measures have enhanced both its carbon efficiency and corporate reputation. Airlines with lower efficiency can particularly benefit from these mechanisms as they gradually invest in longer-term technologies. However, airlines in regions with less stringent environmental policies—such as parts of Asia and North America—tend to exhibit slower progress. The absence of consistent policy support and green financing mechanisms has limited these airlines’ motivation to invest in carbon-reduction technologies, resulting in relatively higher emissions intensity. Policy strategies include:

(1)

Green Technology Subsidies and Tax Incentives

Governments should provide financial incentives—such as subsidies, low-interest loans, or tax relief—to support fleet modernization and the adoption of high-efficiency aircraft and low-carbon propulsion systems. These policies can accelerate the diffusion of cleaner technologies across the industry.

(2)

Sustainable Aviation Fuel (SAF) Promotion

Given SAF’s potential to reduce lifecycle emissions by up to 80%, policymakers should establish dedicated production and procurement mechanisms, such as blending mandates, tax credits, or SAF purchase agreements. These initiatives can lower SAF costs and encourage airlines to incorporate it into regular operations.

(3)

Collaborative Research and Development

Authorities can foster partnerships among airlines, aircraft manufacturers, fuel producers, and research institutions to jointly develop next-generation green aviation technologies, including hydrogen propulsion, hybrid-electric systems, and advanced lightweight materials.

3.3.3. Long-Term Objectives: Supporting Sustainable Aviation Development

Technological innovation is one of the most critical drivers of carbon efficiency improvement in the aviation sector. Continuous fleet modernization, the introduction of new fuel-efficient aircraft, and the adoption of advanced operational technologies have significantly enhanced airlines’ production and operational efficiency. Production efficiency remains the main bottleneck for most airlines. Achieving substantial reductions in carbon emissions requires investments in fleet modernization, adoption of next-generation aircraft, and the accelerated deployment of sustainable aviation fuels (SAFs). For instance, Singapore Airlines (SQ) and Emirates (EK) have both invested heavily in new-generation aircraft such as the Airbus A350 and Boeing 787, which feature reduced fuel consumption and lower carbon intensity. These technological upgrades have enabled them to improve productivity while simultaneously cutting emissions. Governments and international organizations should provide financial incentives, infrastructure development, and coordinated policies to support SAF production and adoption. For example, Finnair (AY) has cooperated with aircraft manufacturers to incorporate biofuels and efficient engine designs into their operations, achieving measurable reductions in carbon output. Such innovations not only enhance carbon efficiency but also strengthen competitive advantages in the emerging low-carbon aviation market.

To achieve deep decarbonization and ensure long-term sustainability, governments must establish comprehensive policy frameworks that integrate environmental goals with industrial growth strategies. Long-term policy directions include:

(1)

Global Coordination for Green Aviation

International organizations such as the International Civil Aviation Organization (ICAO) should continue to strengthen global cooperation through mechanisms like CORSIA (Carbon Offsetting and Reduction Scheme for International Aviation). Harmonized global standards and transparent monitoring systems are essential for achieving consistent and equitable carbon reduction outcomes across regions.

(2)

Investment in Future Aviation Technologies:

Governments should allocate dedicated funds for research on transformative technologies—such as hydrogen fuel systems, electric aircraft, and zero-emission airport infrastructure. These frontier technologies will form the backbone of carbon-neutral aviation in the coming decades.

(3)

Establishment of Long-Term Carbon Reduction Targets:

Policymakers should set clear, science-based carbon reduction targets for the aviation sector and integrate them into national climate strategies. Regulatory frameworks should also include enforcement mechanisms, such as emission penalties or performance-based incentives, to ensure compliance and accountability.

3.3.4. Differentiated Strategies for Airlines with Varying Efficiency Levels

High-efficiency carriers should focus on sustaining technological leadership and further integrating SAF into operations. In contrast, low-efficiency carriers should prioritize production-side improvements, particularly through gradual fleet renewal and the adoption of energy-saving technologies. Regional differences also matter: U.S. airlines need to emphasize technological innovation to improve production efficiency, while Chinese airlines should strengthen operational efficiency to better leverage existing capacities.

Recognizing the heterogeneity among airlines, differentiated policy approaches are needed to support both low-efficiency and high-efficiency carriers effectively.

(1)

For Low-Efficiency Airlines

Governments should provide targeted financial assistance—such as modernization subsidies and low-interest loans—to facilitate fleet upgrades and energy-efficient retrofits. Additionally, training programs in operations management, energy auditing, and carbon accounting can help these airlines strengthen managerial efficiency and close the performance gap.

(2)

For High-Efficiency Airlines

Highly efficient airlines should be encouraged to maintain technological leadership through continued innovation and investment in SAF deployment. Governments can incentivize them with tax benefits, preferential financing, and public recognition programs. Moreover, high-efficiency airlines can be encouraged to share best practices and collaborate with less efficient peers to promote sector-wide improvement.

3.3.5. Integrated Policy Design: A Holistic Approach

The evidence of β-convergence suggests that inefficient airlines are gradually catching up with leaders, but at varying speeds across operational and production stages. Policymakers should therefore promote collaborative platforms that facilitate the diffusion of best practices in management while simultaneously investing in technology pathways for long-term decarbonization.

To achieve meaningful carbon reductions in aviation, policymakers should adopt an integrated and multi-level policy framework that aligns technological innovation, managerial efficiency, and market mechanisms. This approach should include:

(1)

Cross-Sector Collaboration

Governments can promote partnerships between the aviation sector and other industries—such as renewable energy, hydrogen, and digital technology—to accelerate the development of clean energy infrastructure and decarbonization solutions.

(2)

Multi-Level Policy Coordination

Effective coordination is needed among international, national, and regional policies. Global carbon market mechanisms (e.g., CORSIA) should complement domestic emission trading schemes (e.g., EU ETS) to create consistent incentives and avoid policy fragmentation.

In sum, a balanced portfolio of operational optimization, market mechanisms, and technological innovation—supported by targeted policies and international cooperation—will be essential for achieving carbon-efficient and sustainable growth in the global airline industry.

3.4. 2022–2024 Aviation Recovery and Carbon Efficiency

Recent industry reports indicate that the global aviation sector has entered a strong recovery phase since 2022, with passenger demand rebounding rapidly and international traffic approaching or exceeding pre-pandemic levels in many regions. According to recent statistics from ICAO and IATA, air transport activity has shown sustained growth during 2023–2024, accompanied by improvements in load factors and operational performance. However, despite this recovery, several structural challenges related to carbon emission efficiency persist.

First, fuel consumption remains the dominant source of carbon emissions in the aviation industry, and the improvement of fuel efficiency continues to be constrained by technological and operational limitations. Second, the recovery process exhibits significant regional heterogeneity, with airlines in Asia–Pacific and some developing regions recovering more slowly compared to those in Europe and North America. Third, the transition toward sustainable aviation fuels (SAFs) and low-carbon technologies is still at an early stage, limiting the short-term reduction potential of carbon emissions.

These recent developments are broadly consistent with the findings of this study. In particular, the identification of production-stage inefficiency as a key bottleneck and the existence of β-convergence in carbon emission efficiency across airlines remain relevant in the post-pandemic recovery context. The persistence of efficiency gaps across regions further supports the need for differentiated policy measures targeting both technological improvement and operational optimization.

Therefore, although the empirical analysis in this study is based on data from 2015–2021, the results provide meaningful insights into the long-term structural characteristics and evolution patterns of airline carbon emission efficiency, which continue to be applicable in the current phase of industry recovery.

4. Conclusions

This study investigates the carbon emission efficiency of 18 major international airlines between 2015 and 2021 by integrating static and dynamic perspectives within a two-stage superefficient SBM framework and a superefficient SBM-based Hicks–Moorsteen (HM) index. Absolute β-convergence tests are further applied to capture long-term efficiency trends. Several key findings emerge.

Firstly, significant heterogeneity exists across airlines. While carriers such as Singapore Airlines, Finnair, and ANA demonstrate consistently high efficiency, others, including American Airlines and Hainan Airlines, lag behind. On average, operational efficiency exceeds production efficiency, suggesting that technological improvements in fleet and fuel use remain the main bottlenecks for overall efficiency gains.

Secondly, dynamic productivity change exhibited substantial volatility during the study period. The industry-wide downturn in 2019–2020 due to COVID-19 sharply reduced efficiency, yet certain airlines, notably Emirates, Singapore Airlines, and Delta, achieved rapid post-pandemic recovery, for whom auxiliary EC/TC indicators suggest that, from an interpretative perspective, limited technological progress was an important factor associated with productivity declines, whereas managerial improvements directly drove their rapid rebound.

Thirdly, β-convergence is observed in both static and dynamic analyses, implying that less efficient airlines are gradually catching up with efficiency leaders. Notably, convergence occurs faster in operational efficiency than in production efficiency, highlighting the relatively easier diffusion of management practices compared to technological upgrades.

The findings should be interpreted as structural insights rather than real-time performance evaluations. The EC/TC-based interpretative results should be understood as indicative rather than strictly theoretical.

Recent industry reports (2022–2024) indicate that the aviation sector has entered a recovery phase; however, structural challenges such as fuel efficiency constraints and uneven regional recovery persist. These findings are consistent with the patterns identified in this study, suggesting that the conclusions remain relevant in the current context.

The contributions of this study are threefold. Methodologically, it integrates static and dynamic perspectives in a two-stage framework that distinguishes production and operational efficiency. Empirically, it provides updated evidence on efficiency patterns during both normal operations and the COVID-19 shock. Theoretically, it adds to the literature on efficiency convergence in the global airline industry.

From a practical standpoint, the findings suggest that improving production efficiency through fleet modernization and the adoption of sustainable aviation fuels (SAFs) is critical for long-term decarbonization, while operational efficiency can be enhanced more rapidly through digital platforms, route optimization, and improved load management. Policymakers should therefore design differentiated strategies: short-term measures focusing on operational optimization, and long-term strategies prioritizing technological innovation and infrastructure support for SAFs.

It should be noted that maintenance costs were not included in the model due to data availability constraints and comparability issues across airlines. Future research could incorporate more detailed cost structures, including maintenance expenditures, to further improve the accuracy of efficiency measurement.

Strengths include methodological innovation integrating static and dynamic productivity change models, practical relevance incorporating post-pandemic recovery data, and in-depth interpretation of efficiency drivers. Limitations involve a narrow sample scope lacking low-cost carriers and African/South American airlines, insufficient SAF adoption data, and model assumptions less applicable to ultra-large airlines. Future research will expand the sample, collect granular sustainability data, and adopt a meta-frontier framework with machine learning to enhance model generalizability and predictive power.

Overall, the findings should be interpreted as structural insights into airline carbon emission efficiency during 2015–2021 rather than as real-time performance evaluations. Several limitations should be noted. First, the dataset is constrained by public reporting availability, resulting in imbalanced regional representation and limited coverage of low-cost carriers. Second, the sample period ends in 2021 and therefore cannot fully reflect the most recent post-pandemic developments. Third, the HM index and its EC/TC components are used only for interpretative and heuristic purposes and do not constitute a strict theoretical decomposition for two-stage network DEA models. Future research may extend the sample, update the time period, and apply formally consistent dynamic network DEA methods.