How does civil aviation achieve sustainable low-carbon development? — An abatement–cost perspective

Abstract

With the rapid development of civil aviation, carbon emissions have brought severe environmental problems. Realizing efficient and sustainable carbon emission reduction is of great significance for achieving green development in civil aviation sector. Therefore, in the process of pursuing civil aviation carbon emission reduction goals, it is necessary to further consider how to achieve emission reduction at the lowest cost. Based on the accurate carbon emission performance evaluation, the carbon abatement cost among different representative airlines have been systematically compared. The main work and findings of this study can be summarized in the following three aspects. Firstly, a new nonparametric shadow price measurement method was constructed based on the Slacks-Based Measurement Data Envelopment Analysis (SBM-DEA). This can better reflect the essence of efficiency evaluation and the calculated shadow price results are more consistent with the real market. Secondly, the average value of carbon emission efficiency has experienced a fluctuating downward trend from 2011 to 2017, indicating that the carbon emission efficiency of global airlines has decreased. Thirdly, the average value of the shadow price is generally between 313.4 and 398.4 dollars/ton, showing an “up-down-up” trend, and reaching a peak of 398.4 dollars/ton in 2014. This can provide a basis for low-carbon policy makers in the civil aviation sector, and also provide reference for different types of airlines to achieve low-cost emission reduction.

1. Introduction

The incessant emission of greenhouse gases (GHGs) has brought severe environmental and climate problems. Global warming caused by massive GHG emissions has become a great challenge in the 21st century, which seriously restricts the sustainable development of economy. Carbon dioxide (CO₂) emissions, accounting for approximately 77 % of the GHGs, are the primary reason for global warming [1]. In 2019, the global civil aviation industry emitted 0.65 billion tons of CO₂, accounting for about 2 % of anthropogenic carbon emissions (affected by the COVID-19 epidemic, the carbon emissions and other relevant indicators of civil aviation department have been abnormal since 2020) [2]. On the surface, the current proportion and absolute value of carbon emissions from the aviation industry are not much high. However, representative studies have shown that from 2013 to 2019, the global civil aviation carbon emissions have exceeded 70 % of the predicted values of the International Civil Aviation Organization (ICAO) [3]. If not well controlled, CO₂ emissions from global aviation are expected to increase to 1.15–1.61 billion tons in 2050, accounting for almost 25 % of the world's carbon emissions (see Fig. 1) [4]. Therefore, the necessity and urgency of reducing carbon emissions in the civil aviation industry are very prominent.

Fig. 1.

Current status and trend prediction of carbon emissions from civil aviation.

In order to cope with the climate change, civil aviation departments and relevant organizations around the world have made efforts. For example, in 2016, the 39th ICAO Congress passed the historic Carbon Offsetting and Reduction Scheme for International Aviation (CORSIA), forming the first global industry emission reduction market mechanism. The aviation industry has thus become the world's first industry to shift from national regulation to global implementation [5]. It is expected that by 2024, at least 119 countries will participate in the CORSIA. In 2021, the Civil Aviation Administration of China (CAAC) pointed that China's aviation industry will adopt a package of policies (including the airspace optimization, application of new technology, and green civil aviation mechanism) to help achieving the goal of carbon peak in 2030 and carbon neutral in 2060 [6].

The extremely high investment cost, long R&D and application cycle and ultra-high safety requirements in the civil aviation field make it one of the industries with the highest emission reduction costs [7]. However, if carbon emissions from civil aviation cannot be effectively controlled, the economic losses caused will seriously affect the survival and development of the airlines. Taking China as an example, the growth rates of transportation scale and carbon emissions of civil aviation sector are far higher than the global average (see Fig. 1). If the resolution of the CORSIA is followed, the carbon trading expenditure of China's civil aviation sector may reach 21 billion yuan by 2035 [8]. How to effectively address this situation is a difficult problem that aircraft manufacturers and airlines need to face together. Especially for airlines, how to objectively measure the emission reduction costs of different types and regions of airlines is an important issue. Comparing the advantages and disadvantages of major airlines with representative airlines in terms of emission levels and emission reduction costs can provide a more targeted approach to high-quality and low-cost emission reduction in civil aviation sector.

That is to say, civil aviation sector needs to further consider achieving emission reduction at the minimum cost in the process of pursuing the emission reduction target. The existing ideas on studying the emission reduction costs of greenhouse gases and gaseous pollutants can be divided into two categories. The first is post hoc statistics. Through the investigation of the relevant data after the implementation of specific emission reduction measures or policies, the corresponding emission reduction costs can be calculated [9]. The second is prior estimation. Macroeconomic models, such as the Long-range Energy Alternatives Planning system (LEAP) model [10], Computer General Equilibrium (CGE) model [11], and multi-objective planning model [12], are generally used to study the emission reduction costs under different economic and technological scenarios. The distance function method used to calculate the shadow price of pollutants, which serves the above two research ideas, has been widely used. Representative studies include sewage from paper mills [13], sulfur dioxide emitted from power plants [14], or the shadow price of pollutants in different regions of the same industry, such as agriculture in various states of the United States [15], and the power industry in various provinces of China [16].

For the choice of distance function measurement method, most existing studies use parametric model to calculate the shadow price of pollution emissions [17]. This method has many advantages in the results estimation and understanding. Especially for the use of translog stochastic frontier model, which can simultaneously consider the impact of stochastic effect and technical inefficiency on environmental output. Therefore, this type of parametric method has been applied in many fields and obtained fruitful results. For example, a recent study by Ref. [18] applied the translog stochastic frontier model to a sample of 93 coal-fired power plants covering six years. The estimated average shadow prices of CO₂ and SO₂ are 69 $/tonne and 2525 $/tonne. However, this method also has two shortcomings. First, how to set the “correct” functional form is a key challenge faced by empirical research. If the set model does not match the data well or the model has a formal error, the estimated parameters may lead to misleading conclusions [19]. Second, the parametric model method continuously processes data, and cannot obtain the individual output effect of changes in pollutant emissions by economic individuals (such as enterprises). That is, estimated results of parametric models can only obtain an overall average shadow price. However, the shadow price of pollution emissions depends on the productivity level of the emitters themselves. Therefore, there is a certain deviation in the results estimated by the parameter model method [20].

From the perspective of research field, existing studies on the carbon abatement cost in transportation mainly focus on the overall transportation sector. For example, in the study by Ref. [21], the marginal abatement cost of transport sector's CO₂ emission is derived by designing a constrained maximum likelihood model with partial quantile order-α frontiers. Results showed an average marginal abatement cost of CO₂ emission for China's transport sector at around 1009$/tonne. Another representative research by Ref. [9] developed two sets of methods that consider only the energy factor and multiple other factors including energy, to evaluate and analyze the carbon reduction performance of China's provincial transportation sector, identify the provincial patterns of reducing carbon emissions and propose targeted pathways. The results show that both the carbon efficiency and shadow price in the developed eastern provinces are higher than that of the central, western and north-eastern provinces. However, few studies have explored the carbon abatement cost of different transportation modes. Especially for the air transportation, the relevant research is significantly insufficient. Furthermore, the discussion on which airlines should undertake higher (or lower) carbon dioxide emission reduction tasks is even more vacant. This is not conducive to the deployment and implementation of emission reduction policies by the civil aviation department.

In fact, the formulation of carbon emission reduction strategy in the civil aviation sector usually needs environmental efficiency and carbon abatement cost as basis [22]. Because, in terms of carbon abatement cost and emission efficiency, those with relatively lower efficiency and lower marginal emission reduction costs (shadow prices) airlines generally have the ability and potential to undertake more emission reduction tasks [23]. This can help policy makers conduct more targeted and oriented measures, when sharing emission reduction responsibilities [24]. However, research on the carbon emission performance and emission reduction costs of the civil aviation sector (especially for airlines) is relatively poor. Therefore, based on the accurate carbon emission efficiency calculation, this study further analyzes the carbon abatement cost of 15 representative airlines around the world.

As such, the main contributions of this study can be summarized as the following two aspects. Firstly, this study constructs a new nonparametric shadow price measurement method based on the Slacks-Based Measurement Data Envelopment Analysis (SBM-DEA). On the one hand, the technological frontier and the efficiency evaluation of each decision-making unit (DMU) can be obtained by relying on the input-output data, without setting the optimal behavior target of the producer or making special assumptions about the form of the production function. On the other hand, the SBM-DEA model can avoid bias and impact caused by differences in radial and angular selection, in this sense, it better reflects the essence of efficiency evaluation than other models. Based on this, the calculated shadow price results are more consistent with the real market. Secondly, the existing research on the carbon abatement cost in the civil aviation sector is relatively scarce, which is not conducive to the formulation of carbon reduction targets for civil aviation. This study uses the promoted model to accurately measure the carbon abatement costs of the global representative airlines. This can provide a basis for low-carbon policy makers in the civil aviation sector, and also provide reference for different types of airlines to achieve low-cost emission reduction.

2. Methodology

2.1. Carbon emission shadow price

In the framework of shadow price analysis, we usually use distance function to construct environmental production technology. Shephard proposed the original form of distance function, i.e., the Shephard Distance Function (SDF) [25]. On this basis, some studies constructed environmental production technology by using output oriented SDF in trans-logarithm [26]. And then the deterministic parameter method was applied to estimate the parameters of the transcendental logarithm function, thus calculating the shadow price of environmental pollutants. According to the research by Ref. [27], output oriented SDF can be described as Eq. (1):

$$D_0\left(x,y,b\right)=\inf \left\{\theta >0:\left(y/\theta ,b/\theta \right)\in P\left(x\right)\right\}$$ (1)

where $\theta$ represents the value of the output distance function. It represents the maximum value at which output $\left(y,b\right)$ can expand towards the environmental production technology with the given input x.

For the civil aviation department, input indicators generally include fixed capital, labor and energy, and expected output indicators generally include transportation income, transportation scale, available seat kilometers, etc. Undesirable output indicators generally focus on carbon emissions. Similarly, according to the research by Ref. [25], input oriented SDF can be defined as Eq. (2):

$$D_t\left(y,b,x\right)=\sup \left\{\phi >0:\left(x/\phi \right)\in I\left(y,b\right)\right\}$$ (2)

where $\phi$ represents the value of the input distance function. It measures the maximum multiple that the combination of input factors can be reduced towards the environmental production technology with the given output y.

The shadow price calculation formula is generally derived from the dual relationship between distance function and functions of revenue, cost, and profit etc. Specifically, the output oriented SDF and the revenue function are mutually dual; the input oriented SDF and the cost function are mutually dual. Based on the dual relationship, we can apply the Lagrange method and Shephard's lemma to obtain the shadow prices under different orientations, as shown in Eqs. (3), (4):

Output oriented carbon emission shadow price:

$$r_b=r_y\cdot \frac{\partial D_0\left(x,y,b\right)/\partial b}{\partial D_0\left(x,y,b\right)/\partial y}$$ (3)

Input oriented carbon emission shadow price:

$$r_b=r_y\cdot \frac{\partial D_t\left(y,b,x\right)/\partial b}{\partial D_t\left(y,b,x\right)/\partial y}$$ (4)

where $r_b$ represents the shadow price of undesirable output; $r_y$ represents the desirable output shadow price. We generally assume that $r_y$ equals to the market price of the desirable output.

2.2. Shadow price measurement of civil aviation carbon emissions

Recently, some researchers have begun to apply non-radial DEA models to measure the shadow price of undesirable outputs, among which the SBM-DEA type is more commonly used. According to the research by Ref. [28], fixed capital (K) and labor (L) are set as inputs; transportation revenue (Y) is set as desirable output; carbon dioxide emission (B) is set as undesirable output. As such, the expression of SBM-DEA model for airline efficiency measurement can be described as Eq. (5):

$$\begin{array}{l}D=\min \frac{1-\frac{1}{2}\left(\frac{s_k}{K^n}+\frac{s_l}{L^n}\right)}{1+\frac{1}{2}\left(\frac{s_y}{Y^n}+\frac{s_b}{B^n}\right)}\\ \mathrm{s}.\mathrm{t}\text{.}\\ \sum _{i=1}^N{\lambda }_i{K}_i+s_k=K^n\\ \sum _{i=1}^N{\lambda }_i{L}_i+s_l=L^n\\ \sum _{i=1}^N{\lambda }_i{Y}_i-s_y=Y^n\\ \sum _{i=1}^N{\lambda }_i{B}_i+s_b=B^n\\ s_k,s_l,s_y,s_b,\lambda \ge 0\end{array}$$ (5)

where $s_k、s_l、s_y、s_b$ respectively represent slack variables corresponding to fixed capital (K), labor force (L), desirable output (Y) and undesirable output (B); $K^n$、 $L^n$、 $Y^n$、 $B^n$ respectively represent the value of fixed capital, labor force, expected output and unexpected output of the nth airline; $\lambda$ represents the intensity vector. If all slack variables are 0, the environmental production technology is considered to be technically effective. Because Eq. (5) is a nonlinear programming form, it needs to be converted into a linear programming form to facilitate the solution, as shown in Eq. (6):

$$\begin{array}{l}D=\min \left(1-\frac{1}{2}\left(\frac{S_k}{K^n}+\frac{S_l}{L^n}\right)\right)\\ \mathrm{s}.\mathrm{t}\text{.}\\ t+\frac{1}{2}\left(\frac{S_y}{Y^n}+\frac{S_b}{B^n}\right)=1\\ \sum _{i=1}^N{\mu }_i{K}_i+S_k=t{K}^n\\ \sum _{i=1}^N{\mu }_i{L}_i+S_l=t{L}^n\\ \sum _{i=1}^N{\mu }_i{Y}_i-S_y=t{Y}^n\\ \sum _{i=1}^N{\mu }_i{B}_i+S_b=t{B}^n\\ S_k,S_l,S_y,S_b,\mu \ge 0；t>0\text{.}\end{array}$$ (6)

where $\mu =\lambda t，S_k=s_{k}t，S_l=s_{l}t，S_y=s_{y}t，S_b=s_{b}t$. In order to solve the shadow price of undesirable output, the dual form of Eq. (6) should also be described. According to Ref. [29], we hypothesized that $A,p_k,p_l,p_y,p_b$ are dual variables of Eq. (6). The dual form of the above SBM-DEA model is shown as Eq. (7):

$$\begin{array}{l}\max A\\ \mathrm{s}.\mathrm{t}\text{.}\\ A+p_k{K}^n+p_l{L}^n-p_y{Y}^n+p_b{B}^n=1\\ \sum _{i=1}^N{p}_y{Y}_i-\sum _{i=1}^N{p}_b{B}_i-\sum _{i=1}^N{p}_k{K}_i-\sum _{i=1}^N{p}_l{L}_i=0\\ p_k\ge \frac{1}{2K^n}\\ p_l\ge \frac{1}{2L^n}\\ p_y\ge \frac{1}{2Y^n}\\ p_b\ge \frac{1}{2B^n}\end{array}$$ (7)

After solving Eq. (7), we can calculate the shadow price of undesirable output $r_b=r_y{p}_b/p_y$.

3. Date description

This study focused on calculating the marginal carbon abatement cost of the 15 international representative airlines during the period of 2011–2017. The starting year for selecting 2011 as the sample is because the representative global airlines basically recovered from the 2008 financial crisis in 2011 and began to experience a relatively stable operating period [30]. In addition, in 2011, the European Union (EU) announced that from January 1, 2012, all international flights and flights landing within the EU would be granted emission permits. As a result, many airlines hope to improve carbon emission efficiency to balance profit and revenue while meeting the EU's carbon emission reduction requirements. Therefore, accurately measuring the carbon emission reduction costs of airlines since 2011 can provide a theoretical basis for formulating emission reduction policies and responding to international carbon emission reduction pressures. In addition, on May 15, 2018, Delta Airlines, Air France KLM Group, and Virgin Airlines signed a final joint venture agreement, paving the way for the three parties to jointly operate on transatlantic routes. This agreement defines the terms of joint airline operations in terms of management and operations, which significantly impacted the emission reduction costs of these airlines. In particularly, affected by the COVID-19 epidemic [31], the carbon emissions and other relevant indicators of global civil aviation department in 2020 have been abnormal. In order to avoid the impact of those emergencies and special policies on the real shadow price of carbon emissions of airlines, the study period of this study is focusing on the 2011–2017.

Although many governments in non EU countries (such as China and the United States) prohibit domestic airlines from complying with the EU carbon emissions trading system (EU-ETS), major airlines in these countries have implemented important preparatory measures for the EU-ETS. In other words, the inclusion of the aviation industry in the EU emissions trading system has a direct impact not only on European airlines, but also on global airlines [32]. Therefore, from 2011 to 2017, the airlines selected in the sample include both airlines belonging to the EU and non-EU airlines. Considering the availability of data collection and the representativeness of airline samples, 15 representative international airlines were selected as samples for empirical evaluation. The basic information is shown in Table 1.

Table 1.

Basic information of the sample airlines.

Airlines	IATA code	Country	Region
Delta Airlines	DL	America	North America
Southwest Airlines	WN	America
Alaska Airlines	AS	America
Air France KLM	AF	France	Europe
Lufthansa	LH	Germany
Emirates Airlines	EK	The United Arad Emirates	Asia and Oceania
Southern Airlines	CZ	China
Air China	CA	China
Eastern Airlines	MU	China
Hainan Airlines	HU	China
Cathay Pacific	CX	Hong Kong, China
Singapore Airlines	SQ	Singapore
Japan Airlines	JL	Japan
Korean Airlines	KE	South Korea
Qantas Airways	QF	Australia

The selected airlines are from Asia, Oceania, North America and Europe, which are representative airlines of corresponding countries and regions. Airlines in Asia and Oceania have developed rapidly in recent years and become an important part of the international aviation industry. Therefore, for the practical significance of the comparative analysis, most airlines are chosen from Asia and Oceania (9 airlines). In fact, according to the research of [33], most Asian airlines are better than those in other regions in terms of environmental performance. Besides, 14 of the 15 Airlines are among the top 25 in the world in terms of transportation scale (Revenue Passenger Kilometers, RPK). In particular, although the transportation scale of Hainan Airlines is relatively small, its transportation scale has experienced rapid expansion during the study period, so Hainan Airlines can well represent the rapid expansion type of airlines in recent years. Therefore, in general, this sample selection has a great representativeness for global airlines.

In addition, during the study period, the carbon emissions of the sample airlines showed an obvious year-on-year growth trend with the increase of passenger turnover. Among these sample airlines, 6 airlines (DL, EK, CZ, LH, AF and CA) are in the top 10 in terms of transportation scale. At the same time, the overall carbon intensity of these airlines showed an obvious and steady downward trend. From the change characteristics of carbon emissions, the sample airlines are consistent with the development trend of global civil aviation carbon emissions. Moreover, these airlines come from different regions and have obvious regional characteristics. Therefore, these airlines effectively represent the global airlines, and it is appropriate to select them as the research samples.

Due to the particularity of air transport, aircraft must comply with very strict fuel type requirements (mainly subject to fuel storage, fuel economy and safety constraints). Aviation kerosene is the dominant type of energy consumption. A representative study pointed that more than 99 % of total fuel consumption of civil aviation has been jet kerosene since 2014 [34]. Therefore, following the idea of [35], this study assumes that all civil aviation carbon emissions come from jet kerosene combustion. The data on labor force (L), fixed capital (K), and transportation revenue (Y) come from the yearbooks of the assessed airlines, which can be downloaded from the airlines' respective websites. Data on jet fuel and CO₂ emissions come from each airline's annual reports. Table 2 provides descriptive statistics on inputs, outputs and intermediate products from 2011 to 2017.

Table 2.

Descriptive statistics of input-output variables.

Variable	Unit	Average	Median	Maximum	Minimum	Standard Deviation
Labor force（L）	People	53989	46278	128856	8558	33679
Fixed capital（K）	Plane	393	308	856	100	231
Transportation income（Y）	104 dollar	17876	15555	41244	3849	9634
Carbon emission（C）	104 ton	1700	1547	3464	320	814

4. Results and discussions

4.1. Carbon emission efficiency

The traditional radial efficiency analysis model adjusts the desirable and undesirable outputs at the same proportion. This usually leads to the overestimation of the technical efficiency of the decision-making units, but the non-radial efficiency analysis model can overcome this shortcoming [29]. In recent years, some researchers have begun to apply the non-radial DEA model to measure the shadow price of undesirable output, of which the SBM model is more commonly used. Based on the fixed capital, labor, transportation revenue, and carbon emissions indicator data of the 15 representative airlines worldwide from 2011 to 2017, the optimal production frontier of carbon emissions performance for civil aviation can be constructed. The SBM-DEA distance function is used to calculate the efficiency value of carbon emissions for each airline over the years. The detailed calculation results are shown in Table 3.

Table 3.

Carbon emission efficiency values of airlines.

Airlines	2011	2012	2013	2014	2015	2016	2017	Average
MU	0.490	0.502	0.424	0.419	0.380	0.357	0.346	0.417
CZ	0.494	0.511	0.414	0.467	0.389	0.370	0.396	0.434
CA	0.505	0.523	0.487	0.465	0.417	0.410	0.390	0.457
HU	0.545	0.622	0.599	0.655	0.595	0.703	0.685	0.629
CX	1.000	1.000	0.732	0.698	0.593	0.562	0.582	0.738
DL	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
AS	0.733	0.806	0.878	1.000	0.874	0.925	0.792	0.858
WN	0.654	0.687	0.685	0.717	0.748	0.759	0.690	0.706
KE	0.759	1.000	0.751	0.602	0.533	0.532	0.623	0.686
QF	0.546	0.687	0.631	0.602	0.600	0.618	0.531	0.602
AF	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
LH	0.675	0.683	0.625	0.705	0.800	0.798	0.831	0.731
SQ	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
JL	1.000	1.000	1.000	0.928	1.000	1.000	1.000	0.990
EK	0.625	0.666	0.598	0.594	0.540	0.517	0.527	0.581
Average	0.735	0.779	0.722	0.723	0.698	0.703	0.693

As can be seen from Table 3, for different airlines, Delta Airlines, Air France KLM and Singapore Airlines have the highest average annual carbon emission efficiency, with the efficiency values of 1.000 for each year. Japan Airlines was next with an average annual efficiency of 0.990; MU was the lowest, which average annual efficiency value is 0.417. Geographically, the airlines with high annual carbon emission performance are mainly located in North America (including Delta Airlines, Alaska Airlines and Southwest Airlines) and Europe (including Air France-KLM and Lufthansa Airlines); the second is Asia and Oceania (including 6 airlines: Korean Airlines, Qantas, Singapore Airlines, Japan Airlines, Emirates Airlines, and Cathay Pacific Airlines); the lowest are the four major Chinese airlines (including China Eastern Airlines, China Southern Airlines, Air China and Hainan Airlines).

Taking China as an example, as shown in Fig. 2, there is a significant gap in carbon emission efficiency between the four major Chinese airlines and other sample airlines. In recent years, China's civil aviation transportation industry has been in a period of rapid growth, with transportation scale constantly rising. Currently, China has become the second largest air transportation system in the world after the United States. Meanwhile, the European and American civil aviation industries have entered a mature period of industry since the mid-1980s. Compared with the representative European and American airlines (such as Delta Airlines and Air France KLM Airlines), the overall competitiveness of Chinese airlines is still weak, both in terms of technological development and management level [30]. This is also the main reason for the “fault type” gap in efficiency between Chinese airlines and other airlines, showed in Fig. 2.

Fig. 2.

Carbon emission efficiency of airlines in China and other regions, 2011–2017.

In addition, from the perspective of efficiency changes, the carbon emission efficiency of civil aviation in China is not only relatively low, but also has a trend of fluctuating decline. In particular, the efficiency value of China Eastern Airlines has decreased from 0.490 in 2011 to 0.346 in 2017, with a decrease of 29.4 %. The efficiencies of China Southern Airlines and Air China have also decreased by more than 10 %. Compared with the two European airlines, the carbon emission efficiency of AF continues to be efficient (the efficiency value is always 1), while the carbon emission efficiency value of LH has a fluctuating upward trend, which makes the gap between the efficiency level of Chinese airlines and the optimal frontier increasingly wide. This also reflects the fact that in the process of rapid development of Chinese civil aviation, the management level and technical updates cannot match the expansion of the air transportation scale [31]. The carbon emission efficiency related production and operation processes of airlines need to be given sufficient attention by the civil aviation department.

Based on the above analysis and Tables 3 and it is found that the carbon emission efficiency of different airlines varies to degrees, and there is a dynamic change in carbon emission efficiency over time. The gap in carbon emission efficiency between Chinese airlines and other airlines, especially for European airlines, trends to increase. Therefore, this study proposes the following two questions.

• (i) Has the difference in carbon emission efficiency among other airlines narrowed over time?

• (ii) During the sample period, do airlines with low carbon emission efficiency have better improvement performance than those with high carbon emission efficiency?

In order to describe the different evolutionary processes of different types of airlines carbon emission efficiency in the civil aviation sector, this paper adopts the absolute $\beta$ convergence theory to examine the convergence and divergence of carbon emission efficiency of different types of airlines [36]. Specifically, $\beta$ convergence can be obtained by the following regression analysis model:

$$\ln (y_{i,t}/y_{i,0})=\alpha +\beta \ln \left(y_{i,0}\right)+{\epsilon }_{i,t}$$ (8)

where $y_{i,0}$ and $y_{i,t}$ respectively represent the efficiency values of the ith airline in period 0 and period t; $\ln \left(y_{i,t}/y_{i,0}\right)$ represents the carbon emission efficiency growth rate of the ith airline from period 0 to period t; $\alpha$ represents the intercept term constant, which is used to indicate the stable state of technological progress of the airline; $\beta$ indicates the coefficient of carbon emission efficiency of the civil aviation sector; ${\epsilon }_{i,t}$ represents a random perturbation term. When the value of $\beta$ is less than 0, it indicates that the growth rate of carbon emissions performance of each airline is reversed from its initial performance level, i.e., there is convergence, and vice versa.

For regression analysis of panel data, it is necessary to determine whether to choose a fixed effect model or a random effect model. Therefore, before using Eq. (8) for regression estimation, this study uses the Hausman test to examine the panel data of the civil aviation sector, and the results show that the fixed effect model is more suitable (for details see Ref. [37]). The detailed estimation results are shown in Table 4.

Table 4.

Convergence results of carbon emission efficiency of airline.

Parameter	All samples	China	Asia	Europe	North America
$\alpha$	−0.0063 （−1.8904）	−0.0196* （−1.9421）	−0.0065 （−1.0431）	−0.0023 （−0.8085）	−0.0042** （−1.7903）
$\beta$	−0.4214*** （−6.3894）	−1.8532*** （−2.6027）	−0.4532*** （−3.1021）	−0.3624*** （−5.2187）	−0.7763*** （−8.7438）
Adjusted $R^2$	0.7733	0.5611	0.8541	0.4401	0.8134

Note: t-statistics in parentheses.

***, **, and * indicate the significance levels of 1 %, 5 %, and 10 %, respectively.

As is shown in Table 4, including China Airlines, Asian Airlines, European Airlines, North American Airlines, and all sample airlines, the regression coefficients of $\beta$ are all negative and pass the significance level of 1 %. This indicates that there is an absolute $\beta$ convergence of carbon emission efficiency among airlines in different regions. The improvement rate of carbon emission efficiency of airlines with low carbon emission efficiency levels is higher than that of airlines with high performance levels. There is a “catch up effect” between low levels and high levels, and the carbon emission performance levels of various airlines tend to converge. The regression coefficient ($\beta$ value) indicates that the convergence rate and convergence of Chinese airlines are faster, followed by Asian and North American airlines, and European airlines are the slowest. In the future, in order to further promote the convergence of carbon emission efficiency and narrow the differences in carbon emission efficiency, it is necessary to take certain policy measures. For example, airlines should be encouraged to exchange and communicate experiences in carbon emission reduction technology, operation management, and other aspects. Thus, realizing the diffusion of advanced emission reduction technologies and operating concepts in those developing civil aviation regions.

4.2. Carbon abatement costs

According to the calculation, the transportation revenue of the sample airlines increased from 24.878 billion dollars in 2011 to 29.025 billion dollars in 2017, with an average annual growth rate of 2.60 %. Meanwhile, carbon emissions increased from 226 million tons in 2011 to 291 million tons in 2017, with an average annual growth rate of 4.30 %. Dynamically, the growth rate of carbon emissions and the growth rate of transportation revenue have roughly the same trend in the civil aviation industry. A research by Ref. [38] drew the similar conclusions using the Tapio decoupling model. It can be seen that carbon emission reduction in the civil aviation sector will incur a certain economic cost. An additional reduction of one unit of carbon emissions will cause economic losses, that is, the marginal emission reduction costs. Table 5 shows the shadow price of carbon emissions of 15 airlines from 2011 to 2017.

Table 5.

Shadow price of airlines’ carbon emission reduction (unit: dollar/ton).

Airline	2011	2012	2013	2014	2015	2016	2017	Average
MU	331.6	346.4	312.9	298.2	264.9	237.4	239.1	290.1
CZ	357.6	368.9	320.8	334.6	258.1	228.7	259.7	304.1
CA	360.3	359.4	338.6	321.2	280.6	253.0	252.2	309.3
HU	341.0	361.7	351.6	367.7	337.7	193.5	454.5	343.9
CX	56.7	18.3	216.1	191.1	251.8	230.5	129.6	156.3
DL	278.7	261.7	365.2	531.3	208.5	145.9	48.7	262.9
AS	352.8	411.6	466.1	1190.1	460.8	457.6	428.0	538.1
WN	313.1	342.3	283.8	371.6	375.0	368.0	372.3	346.6
KE	173.3	50.5	246.0	205.4	255.2	246.0	181.1	193.9
QF	358.2	398.4	348.4	315.1	294.3	288.0	282.6	326.4
AF	270.7	298.0	322.6	252.8	235.5	230.3	216.8	260.9
LH	347.6	385.0	388.6	385.7	400.5	386.8	368.2	380.3
SQ	186.8	153.7	107.1	193.0	100.6	76.9	163.9	140.3
JL	852.2	1081.7	1408.4	680.3	1179.2	1089.3	1200.8	1070.3
EK	312.8	363.6	356.5	337.8	301.5	269.7	267.8	315.7
Average	326.2	346.7	388.8	398.4	346.9	313.4	324.3	349.2

Note: The average data in the table were calculated from the original data and rounded off.

The shadow price reflects the reduction in expected output caused by reducing undesired output. The larger the value, the more important it is to obtain and increase desirable output as a scarce resource. The calculation results show that the annual average value of the shadow price of carbon emission of sample airlines from 2011 to 2017 is 349.2 dollar/ton. This means that each ton of carbon emission reduction in the civil aviation sector will lead to a decrease in transportation revenue of 349.2 dollars (based on the constant price in 2011), indicating that carbon dioxide has a significant constraint on the economic development of the civil aviation sector. This further proves that carbon dioxide is a competitive allocation of resources, which requires macro allocation of global civil aviation departments [39].

The significant difference in carbon dioxide shadow prices among airlines indicates that the marginal carbon abatement costs of airlines in different countries are different. The emission reduction costs of 9 airlines including Southern Airlines, Air China, Hainan Airlines, Alaska Airlines, Southwest Airlines, Qantas Airlines, Lufthansa Airlines, Japan Airlines and Emirates Airlines all exceed 300 dollars/ton, among which Japan Airlines’ emission reduction cost was more than 1000 dollars/ton. Cathay Pacific Airways, Korean Airlines and Singapore Airlines have relatively low carbon emission reduction costs, all of which are less than 200 dollars/ton, among which Singapore Airlines has the lowest carbon abatement cost. By comparison, existing studies measured that the national average carbon abatement cost was 5570 yuan/ton and 14300 yuan/ton, respectively [40]. It can be found that, compared to other sectors, the cost of reducing carbon emissions in the civil aviation sector is relatively lower than that in the industrial sector. But it still belongs to the industry with high carbon abatement costs.

From a regional perspective, there are significant differences in the carbon abatement cost from civil aviation among different regions. The four major airlines in China have the lowest carbon emission reduction costs, with an average annual carbon abatement cost of 311.85 dollars/ton, followed by two European airlines with an average annual carbon abatement cost of 320.65 dollars/ton. Combining the above carbon emissions and carbon emission efficiency, the airlines with high carbon emissions and low carbon emission efficiency have lower marginal emission reduction costs. Therefore, from the economic point of view, China's four major airlines have greater emission reduction potential and motivation.

As shown in Fig. 3, the average carbon abatement cost of the 15 sample airlines in 2011∼2017 was between 310 and 400 dollars/ton, experiencing an “up-down-up” fluctuation trend. From 2011 to 2014, the carbon abatement cost continued to increase, reaching a peak of 398.4 dollars/ton. Although since 2014, the carbon abatement cost in the civil aviation sector has shown a significant downward trend, falling to 313.4 dollars/ton in 2016, the shadow price of carbon emissions has rebounded since 2016 and increased to 324.3 dollars/ton. This result indicates that the cost of carbon emission reduction has been increasing on the whole before 2014, but with the gradually maturity of emission reduction technology in this industry, the carbon abatement cost has begun to decrease after 2014. However, considering the increasing difficulty of carbon emission reduction technology progress in the civil aviation sector, the cost of carbon emission reduction in the civil aviation sector will not have a significant downward trend in the short term. This is also the main reason for the rebound of carbon abatement cost since 2016.

Fig. 3.

Average carbon abatement costs of the sample airlines over the years, 2011–2017.

Similar to the convergence of environmental efficiency for carbon emissions in the civil aviation sector, we further focus on analyzing the coefficient of variation (CV) and convergence of the shadow price of carbon emissions for airlines. The specific results are shown in Table 6.

Table 6.

Average emission reduction cost and CV of sample airlines.

Airline	Average abatement cost (dollar/ton)	Ranking	Coefficient	Ranking
MU	290.1	6	0.140	6
CZ	304.1	7	0.167	8
CA	309.3	8	0.141	7
HU	343.9	11	0.208	10
CX	156.3	2	0.536	14
DL	262.9	5	0.548	15
AS	538.1	14	0.499	13
WN	346.6	12	0.095	2
KE	193.9	3	0.340	12
QF	326.4	10	0.123	4
AF	260.9	4	0.136	5
LH	380.3	13	0.042	1
SQ	140.3	1	0.300	11
JL	1070.3	15	0.207	9
EK	315.7	9	0.114	3

Combining Table 6 and Fig. 4, we find that the CV of sample airlines’ carbon emission shadow price increased from 2011 to 2013, but after a short decline in 2013∼2014, it has experienced a significant increase since 2014.

Fig. 4.

Coefficient of shadow price of carbon emissions for sample airlines, 2011–2017.

Specifically, the CV of sample airlines' carbon abatement cost reached the highest value of 0.79 in 2017, and reached the lowest value of 0.5 in 2011. In response to the convergence of environmental efficiency values for carbon emissions, the convergence of shadow prices for carbon emissions from 15 sample airlines increased during the period of 2011–2013, but this process has been suppressed since 2014. This indicates that the differences in carbon abatement cost from various airlines have been widening continuously since 2014. In addition, according to the ranking of the CV of each airline's carbon abatement cost, the shadow price of carbon emissions from various airlines showed different convergence in 2011–2017.

The coefficients of variation for the shadow price of carbon emissions from Cathay Pacific Airlines, Delta Airlines, and Alaska Airlines are relative large (between 0.499 and 0.548), indicating that the carbon abatement costs of these airlines have significantly changed from 2011 to 2017. Taking Cathay Pacific Airlines and Delta Airlines as an example, the shadow price of Cathay Pacific Airlines increased from 56.7 dollars/ton in 2011 to 251.8 dollars/ton in 2015, an increase of 3.44 times. However, the carbon abatement cost of Delta Airlines dropped from 531.3 dollars/ton in 2014 to 48.7 dollars/ton in 2017, showing a significant reduction trend. The development stage of different airlines determines their transport demand and development level of carbon emission reduction technology. There are significant differences in the carbon abatement cost among airlines in the civil aviation sector, and differentiated emission reduction measures should be formulated. For the airlines with high coefficient of variation of carbon abatement cost (such as Lufthansa, Southwest Airlines, Emirates Airlines, Qantas, etc.), their carbon abatement costs have relatively little change during the study period. This means that the economic costs of carbon emission reduction for these airlines have not fluctuated significantly.

5. Conclusions and implications

5.1. Conclusions

Realizing efficient and sustainable carbon emission reduction is of great significance for achieving green development in civil aviation. In the process of pursuing civil aviation carbon emission reduction goals, it is necessary to further consider how to achieve emission reduction at the lowest cost. Based on the accurate carbon emission efficiency calculation, this study analyzes the carbon abatement cost of 15 representative airlines around the world from 2011 to 2017. In addition, a horizontal comparison of the carbon abatement cost among airlines was conducted. The main research contents and conclusions of this study are as follows.

First, a new non-parametric carbon abatement cost model was constructed for the civil aviation sector. To measure the carbon emission efficiency of the sample airlines, the fixed capital and labor force were treated as inputs, the transportation revenue was treated as desirable output, and the carbon emission was treated as undesirable output. Based on the SBM-DEA model, this study puts forward an airline carbon emission shadow price calculation model, and calculates the carbon abatement cost of 15 representative airlines in the world from 2011 to 2017.

Second, the average values of carbon emission efficiency of 15 airlines showed a fluctuating downward trend from 2011 to 2017. Specifically, Delta Airlines and Air France KLM Airlines have the highest annual carbon emission efficiency, followed by Japan Airlines. From a geographical perspective, airlines in Europe and North America have the highest annual carbon emission performance. In particular, there is an obvious efficiency gap between China's four major airlines and the others. Dynamically, airlines with low carbon emission efficiency have the higher improvement rate than those with high efficiency levels, experiencing a “catch up effect”.

Third, the average carbon abatement cost of sample airlines was between 313.4 and 398.4 dollars/ton, showing an “up-down-up” trend. Due to the increasing difficulty of potential emission reduction technologies, the decline of the carbon abatement cost in the global civil aviation will be small. From a regional perspective, China's four airlines have the lowest carbon emission reduction costs, followed by two European airlines and Asian airlines. Correspondingly, China's airlines have the greatest carbon emission reduction potential. In addition, the sample airlines achieved a certain degree of divergence in the carbon abatement cost, and differentiated emission reduction measures should be formulated.

5.2. Policy implications

Civil aviation urgently needs to get rid of the current development status of high carbon abatement cost. Based on the conclusions above, this study offers the following policy suggestions.

From an efficiency perspective, improving the carbon emission efficiency can effectively cut back inputs and realize carbon emission reduction. Global civil aviation department should take actions to improve the carbon emission efficiency. For example, airlines can optimize scheduling and route network to reduce invalid flights and improve operation efficiency. Additionally, airlines need to timely adjust the fleet structure including retiring old aircrafts and updating new energy-saving aircrafts, and match proper aircraft types with the flight ranges to avoid high fuel consumption caused by resources misallocation. Moreover, airlines should cooperate with the air traffic control department to summarize and formulate detailed procedures in fulfilling fuel-saving technology, thus reducing ineffective fuel consumption caused carbon emissions.

Second, from the perspective of technological progress, advanced technologies should be constantly introduced and implemented to reduce carbon abatement cost of the civil aviation. The share of traditional jet fuel should gradually be tapered, and cost-effective decarbonization technology should be promoted. For example, promoting the sustainable aviation fuel (SAF) is a feasible path. The large air transportation countries, such as US and China, can contribute to the use of SAF by levying a carbon tax or increasing renewable energy subsidies. Moreover, airlines in different countries should be encouraged to enhance their green technology spillover through international trade, cross-border mergers and acquisitions etc. In this case, the technical exchange and mutual learning between airlines can form a virtuous circle worldwide and contribute to the acceleration of the pace of solving global climate problems. Thus, in the long run, the cost of civil aviation carbon emission reduction will be significantly reduced.

Third, the carbon abatement costs of airlines vary among different regions and development levels. Achieving the goal of reducing carbon emissions in civil aviation requires long-term targeted planning adjustments and strategic layout. For example, emerging airlines, represented by China, need to further improve their carbon emission efficiency in order to achieve a reduction in emission reduction costs. Meanwhile, airlines with high carbon emission performance, represented by Japan Airlines (JL), have relatively high carbon abatement costs, and can achieve technological progress by increasing R&D investment, thus promoting sustainable green development of airlines.

5.3. Limitations and future directions

There are still some limitations of this study. First, due to the impact of the COVID-19 pandemic that erupted in 2020, we have to rule out the exogenous event in our study process of carbon abatement cost evaluation. So this study dismisses this period and fails to obtain the latest research data. In the future, we can expand the sample size and focus on the impact of airlines' emission reduction costs in the context of COVID-19. Second, from the perspective of method design, as a deterministic linear programming method, SBM-DEA based carbon abatement costs method cannot consider the problem of random errors. The Convex Nonparametric Least Squares (CNLS) and Stochastic Nonparametric Envelopment of Data (Sto NED) can overcome this defect, and some researchers have also begun to use them to calculate the shadow price of undesirable outputs [24]. However, such methods also require a large amount of data and have not been widely used in the existing literature. Therefore, how to construct a more suitable model to calculate abatement costs, especially for the civil aviation sector, is a direction that needs further research in the future.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Xiao Liu: Conceptualization, Data curation, Formal analysis, Funding acquisition, Supervision, Writing – review & editing. Pengcheng Jiang: Data curation, Methodology, Software, Writing – original draft.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.