The Approach to Carbon Emission Quotas of Road Transportation: A Carbon Emission Intensity Perspective

Carbon trading is an effective measure for the road transportation to reduce energy consumption and carbon emissions. Carbon emission quotas are the primary concern to ensuring the efficiency of carbon trading. However, the existing studies have mostly focused on carbon emission quotas in different regions, i.e., countries and provinces. Few literature studies simulate carbon quota allocation in the road transportation. A novel approach from the perspective of carbon emission intensity of vehicle is proposed, on the basis of data envelopment analysis (DEA) model. Unlike other studies, the idea of allocation of baseline excitation is introduced and the intensity is included in the model as the baseline. Firstly, the Delphi method is employed to select input and output indicators. Secondly, carbon emission intensity is determined by the cumulative distribution function (CDF). Furthermore, the carbon emission quotas in road transportation in 30 provinces of China are used to validate the model. *e results show that (1) the carbon emission intensity of commercial trucks and buses in China’s road transport industry is 75.04 g/t·km and 13.12 g/p·km, respectively; (2) the provinces of Shanghai, Guangdong, and Xinjiang have the greatest carbon reduction potential and Henan, Hunan, and Anhui have the largest increase in emission quotas; (3) compared with traditional “history responsibility” and “baseline” methods, the proposed approach increases allocation efficiency by 19% and 14%, respectively; and (4) the approach can make the carbon emission quotas play the role of incentive while taking fairness into account and can more effectively promote the implementation of carbon trading system in road transportation.


Introduction
China has become the largest carbon emission country in the world and promised to reduce the intensity of carbon dioxide emissions per unit of GDP in 2020 by 40% to 45% from 2005 and to reach peak carbon emissions in 2030 [1,2]. However, China is facing pressures in the international negotiation on CO 2 emission control and climate change mitigation, in terms of the following aspects, including the growing emphasis on international environmental issues from the public and the government, the increasing demand for energy and resources in the development of economics, and the fact that a perfect carbon reduction mechanism has not been well established [3,4]. Carbon trading is an important means for China to achieve the goal of carbon emission reduction, and its fundamental idea is to use market means to regulate carbon emissions. China issued the Plan for the Construction of the National Carbon Emissions Trading Market (Power Generation Industry) in 2017, marking the official launch of the national carbon trading market in China.
As an industry with the highest oil consumption and the most rapid growth in energy demand and carbon emissions, transportation is in need of improved energy efficiency and low-carbon development. In 2018, the road transportation recorded a total operating passenger volume of 13.672 billion persons and a total operating freight volume of 39.569 billion tons, accounting for 76% and 78% [5], respectively, of the total transport volume, as shown in Figure 1. e road transportation is the main component of transportation and the key area of energy consumption and carbon emissions. In order to realize the carbon reduction commitment, how to establish the carbon trading mechanism to measure and manage road transport emissions has become an urgent issue to be solved. Here, a scientific allocation of the emission quotas is essential for establishing the carbon trading mechanism of the road transportation.
Carbon emission quotas directly determine the operational efficiency of the carbon trading market, which has attracted wide attention from scholars all over the world [6][7][8].
e carbon emission quota allocation is a kind of special resource allocation process in which reasonable methods are applied to allocate the total quotas across the provinces.
In terms of study directions, there are two main directions including the fairness principle-based research and the efficiency principle-based research. In the fairness principle-based research, some classic models are widely used, such as the "historical responsibility" model and the "baseline" model. In other research studies, the models targeted to distribution efficiency are studied, i.e., the DEA-(data envelopment analysis-) related models. e fairness principle will probably affect distributive efficiency and incentives. And the efficiency principle will probably affect the fairness, which might cause implementation difficulty and fierce resistance from companies. ere are few studies that can combine the efficiency, the fairness, and the incentives.
In terms of application industries, there are some differences between the road transportation and the other industries. Vehicles are the main source of energy consumption and carbon emissions. Carbon emission by mobile point sources, as in the road transportation, is more difficult to monitor than emission by fixed-point source, as in the electricity and steel industries. e road transportation has certain difficulties in the scientific allocation of initial quotas. e first is the collection of carbon emission data of enterprises. e second is the selection of the indicators for the road transport industry which affect the allocation of initial allowances for carbon emission. e third is the demarcation about the baseline of vehicle carbon emission intensity for the road transport industry. At present, few scholars have conducted research on the road transportation.
According to the above, it is urgent and necessary to put forward a quota allocation model which can combine the fairness, the efficiency, and the incentive, conforming to the features of road transportation industry. Carbon emission intensity of vehicle is an important characteristic index of mobile source emission, which can effectively represent the carbon reduction potential and incentive effects. For this reason, we carry out the research on the approach for carbon emission quotas of road transportation from a carbon emission intensity perspective.
In this article, the DEA is utilized to address the carbon emission quota allocation problem in the Chinese road transportation. e DEA methodology can handle desirable and undesirable outputs simultaneously, which is highly fitted with the circumstance of carbon emission quota allocation problem. However, due to the point of the DEA that is put on the efficiency, the fairness and the incentive may be ignored. To solve this problem, we introduce the baseline of vehicle emission intensity into the DEA framework. To this end, firstly, we establish a comprehensive BL-DEA (baseline DEA) model by theoretical analysis. Secondly, the Delphi method is employed to select input and output indicators.
irdly, carbon emission intensity is determined by the cumulative distribution function (CDF). Finally, the carbon emission quotas in the road transportation in 30 provinces of China are used to validate the model.
Our research is expected to be helpful for the more scientific allocation of road transportation carbon emission quotas to the provinces of China and promote the development of the carbon trading market in China. e rest of this paper is organized as follows: Section 2 reviews relevant literature. Section 3 introduces the carbon emission quota model, the selection method of indicators,  and the cumulative distribution function of emission intensity. Section 4 carries out data analysis and simulation calculation. Finally, Section 5 contains the conclusions and shortcomings of this study which provides guidance for further work.

Literature Review
is article focuses on the approach for the carbon emission quota allocation problem in the road transportation. In the carbon emission quota allocation, there are mainly two relevant research directions, including the fairness principlebased methods, such as the "historical responsibility" model and the "baseline" model, and the efficiency principle-based methods, i.e., the DEA-related models.

Fairness Principle-Based Quota Allocation Methods.
According to the fairness principle, carbon emission quotas could be allocated in proportion to the historical emissions, the population, the emission intensity, and so forth. In 1986, the American economist Dales first proposed the concept of carbon trading [2] and pointed out that the world needs to establish a pollutant emission system. Under such system, each country will have the corresponding emissions and be issued with the emission permit so that it can trade the emissions like commodities. Carbon trading is designed to reduce carbon emissions. erefore, the primary criterion for evaluating the carbon trading mechanism is environmental effectiveness, i.e., the level of carbon emission reduction [9]. e total amount of initial allowance allocation largely determines the level of carbon emission reduction. Dales employed different models to evaluate the level of carbon emission reduction in the EU, finding out that the excessively loose total amount of initial allowances is the most major factor affecting carbon emission reduction [6,7]. Boehringer et al. [8] also calculated the total amount of carbon allowances, and the results showed that the excessively loose carbon allowances will have a serious negative external impact on carbon emission reductions. erefore, the issue of initial allowance allocation has become the first issue to be resolved in the carbon trading mechanism.
In order to address the issue of the allocation of initial allowances for carbon emission, Westing [10] suggested that the area of land could be used as a measure for allocating emissions. Jensen and other scholars proposed a historical emission-based allocation model [11], i.e., the historical responsibility allocation model combining the historical responsibility for CO 2 emissions in various regions with the policy objective of allocating future emissions. Grubb [12] proposed a modified model of average distribution based on the population, under which everyone should have equal rights and be allocated with equal emission allowances. Kverndokk [13] also advocated the allocation of carbon emissions by the population size of the social subject participants. Yi et al. [14] believed that the principle of sustainable development is of great significance to constructing a common but different scheme for regional allocation of carbon allowances. Yu et al. [15] proposed another concept of cumulative per capita emission, advocating the idea of equal or convergent cumulative per capita emission over a period of time. However, the above models are humancentered and ignore the fact it is governments that are responsible for carbon emissions, leading to deviations in allocation targets. e baseline method was thus proposed to solve the problems. Under the baseline method, allowances are allocated based on the standard emission rate for an industry, i.e., enterprises with better emission reduction performance gain more benefits through allowance allocation. Gagelmann [16] studied the impact of historical responsibility and baseline method on the liquidity of the carbon trading system, carbon price fluctuations, and corporate investment. It was found that compared with the "historical responsibility," the "baseline method" can better stimulate the liquidity of the emission trading system and affect the future development of the carbon trading system through the expected effect of enterprises. e allocation of initial allowances for carbon emission is a complex system issue that involves multiple aspects. erefore, many integrated allocation models and allocation schemes have gradually matured. For example, Filar and Gaertner [17] used nonlinear programming and Shapley values to apportion worldwide carbon emission reduction responsibilities. Eyckmans and Tulkens [18] adopted a cooperative game approach to discuss the issue of the sharing of emission reduction responsibilities among different countries. Viguier et al. [19] employed a two-level computable general equilibrium model to study the allocation of emission allowances among EU member states. Phylipsen et al. [20] proposed a trinity partial method to distribute emission reduction burdens among EU member states. Groenenberg et al. [21] expanded the trinity partial method to the whole world. Den Elzen et al. [22,23] further proposed a multiphase commitment method that allows delayed participation of developing countries. Other scholars such as Bohringer et al. [24] and Ekholm et al. [25] proposed that the selection of emission reduction indicators should emphasize the anthropogenic reduction of CO 2 emissions and the fair allocation among countries. rough such two factors, the total amount of CO 2 emission reduction could be derived. Baer [26] also used the product of GDP per capita and cumulative emissions per capita as a fairness indicator in the GDR scheme. BJ-Tang et al. [27] proposed a reasonable and effective allocation scheme for the government with traditional methods from the industry perspective. e results showed that the quotas of the grandfathering scheme are larger than those of the benchmarking scheme. Rong Han et al. [28] examined the allocation of carbon quotas in the Chinese road transportation and forested the vehicle possession using a gray forecast model and trend extrapolation. e finding was that both the vehicle possession in the road transportation and the corresponding carbon emission present the trend of growth.
ere are some limitations about the fairness principlebased quota allocation methods. For instance, under the "historical responsibility" allocation model, it is difficult to accurately calculate the due allowances for newcomers in the market. Furthermore, there would be such a phenomenon Journal of Advanced Transportation that enterprises with many carbon emissions are allocated with many allowances, while those making technical improvements to reduce carbon emissions are allocated with few allowances.
is would possibly lead to incentive distortions.
e "baseline method" has strong industry characteristics and can accurately match an industry's regulatory needs, giving effective play to the subjective initiative of enterprises' independent emission reduction. However, the reasonable selection of the industry baseline is supported by a large amount of actual industry data that are usually difficult to collect.

Efficiency Principle-Based Quota Allocation Methods.
e quota allocation methods based on the fairness principle will probably affect distributive efficiency. e efficiency is an essential factor of a practical quotas allocation method. Hence, some scholars conducted research on the allocation methods based on the efficiency principle. e research of Wang pointed out that the allocation of initial allowances for carbon emission can be considered as a cost allocation problem under total control [4]. erefore, a data envelopment analysis (DEA) based on operations research can be used to establish an allowance allocation model under which several input/output parameters are set as constraints to solve the allowance allocation problem. Cook and Kress [29] put forward a model under the DEA framework to deal with the fixed input allocation problem. Given the limited total allowances, Lozano and Villa [30] and Lozano et al. [31] also studied such problems as the allocation of emission permits. Lins et al. [32] introduced the idea of zero-sum game to solve the problem that decision units in the DEA model were independent from each other and proposed an improved ZSG-DEA model. Lin and Ning [33] used the ZSG-DEA model to study the efficiency of allowance allocation among European countries in 2009. Pang et al. [34] studied, basing on the ZSG-DEA model, how to maximize the efficiency of allowance allocation among countries. Feng et al. [35] employed the centralized allocation model based on improved DEA to study the allowance allocation among OECD countries under the hypothesis of constant scale returns and variable scale returns. Chiu et al. [36] adopted the ZSG-DEA model of superrelaxed basis measurement to study the initial allowance allocation among EU countries, clarifying how to maximize the allocation efficiency. When using the DEA model to solve the problem of allocation of trading allowances for carbon emission, it is important to deal with the undesirable output of carbon emissions. Chung et al. [37] and Zhou et al. [38] employed the directional distance function to obtain the optimal solution of DEA by increasing necessary output and reducing unnecessary output. Seiford and Zhu [39] adopted the method of converting unnecessary output into ideal mathematical output under the condition of classification invariance. Reinhard et al. [40] and Zhang et al. [41] chose to treat unwelcome outputs as input, and Sueyoshi et al. [42,43] proposed the usage scale adjustment measures to deal with undesired and expected results in a unified manner.

Contribution of is Paper.
From the above review, it can be seen that scholars have conducted a great deal of research on the allocation of emission quotas. But the following problems remain. Firstly, current research has focused more on national or provincial allocation, while few scholars carried out research on the road transportation. Although Han et al. [28] analyzed the carbon emission quotas in the Chinese road transport sector from the perspective of carbon trading and designed a carbon trading mechanism, the research focused more on the calculation of the total amount of carbon quotas under different policy scenarios and on the macro policies. Secondly, the existing DEA model fails to consider the performance incentives for emission reduction based on the emission intensity and thus is not conducive to improving the efficiency in emission reduction in industry development.
On this basis, this paper analyzes the carbon emission quotas in the Chinese road transportation from the perspective of emission intensity and pays more attention to the allocation between the provinces. e research introduces the vehicle emission intensity as the baseline to establish an improved BL-DEA model, with the following contribution.
Firstly, we propose an approach for the carbon emission quotas of the road transportation, which takes the fairness, the efficiency, and the incentive among all participators into account. Specifically, the consideration of the fairness makes the generated allocation mechanism easier to accept. e introduction of baseline theory has brought about a significant incentive effect. Meanwhile, the application of DEA ensures the distributive efficiency.
Secondly, through the statistical analysis of the vehicle data, we identify the baseline of carbon emission intensity by the use of the cumulative distribution function. is solves the problem that the baseline of road transportation is hard to determine, which can provide a reference for the carbon emission level assessment.
irdly, the proposed approach is applied to the empirical study of the quotas of allocation in the road transportation to 30 provinces of China.
To conclude, this paper presents a feasible way for the Chinese government to achieve the carbon emission reduction target. In theories, this article develops a new approach to address the carbon emission quotas allocation problem. In practice, it solves a real-world problem by providing practical findings and implications.

BL-DEA Model.
e premise of carbon trading for road transport is the benign development of the industry cannot be affected. erefore, the allocation of initial quotas must reflect efficiency and fairness. e ultimate goal of reducing the carbon emission requires incentives to be present. e BL-DEA model is established based on the following principles: (1) Prioritize the development of the industry, i.e., the initial allowance allocation must maximize the overall efficiency (2) Under the initial allowance allocation plan of each enterprise, the total allowance must be fully allocated (3) Reflect the idea of performance incentive, i.e., initial quotas allocation must be combined with the baseline of emission intensity Beasley [44] pointed out in his research that in order to maximize the overall efficiency of the allocation objects, decision-makers can use the average efficiency optimization instead of the single DMU (diesel multiple-unit) efficiency in the traditional DEA model.
Assume that there are a total of n DMU q (q � 1, 2, . . . , n) of the same type, each of which has m types of output and p types of input. We use y rq to represent no. r(r � 1, 2, . . . , m) output of DMU q and use x iq to represent no. i(i � 1, 2, . . . , p) input of DMU q ; u r represents the weight coefficient corresponding to no. r output, and v i represents the weight coefficient corresponding to no. i input; e q represents the efficiency of DMU q . We take the initial allowance for carbon emission of DMU q as a special input, represented with f q . We use F to represent the total amount of allowances to be allocated. According to Beasley's research, we use the average efficiency maximization as the objective function and can get the following model: (1) In model (1), E is the objective function, which maximizes the average efficiency; the first constraint describes the calculation method of e q ; the second and third constraints describe the value range of e q u r and v i , and the last constraint describes the total amount of allowances that have been allocated.
We assume that the optimal solution of the objective function is E * , and it is easy to prove that the result of model (1) is (weak) valid for DEA, that is, the solution E * � 1 exists, which is proven as follows.
(2) In order to obtain a scientific allocation method forf q , we take the optimal solution E * � (1/n) n q�1 e q � 1 of model (1) (3) In model (3), max f q and min f q are used as objective functions to calculate the maximum and minimum optimal solutions, respectively. e last constraint guarantees that the value of f q meets the requirement of optimal efficiency. e other constraints are the same as model (1). We record the minimum optimal solution obtained by model (3) as S q and the maximum optimal solution as L q . In general, S q < f q < L q , If S q � f q � L q exists in DMU, and it means that the allocation result of the DMU has been determined.
In order to reflect the incentive effect of carbon emission intensity of vehicle in the model, we need to consider combining the DEA model with the baseline of emission intensity. We make the value of f q close to the value allocated under the baseline of intensity, as much as possible. f q0 is represented as the initial quota value allocated under the baseline method. Based on the above, we can get the following model: (4) In model (4), the objective function is meant to get f q as close as possible to the f qo . e last constraint guarantees that the value of f q lies between the maximum and the minimum optimal solution. e other constraints are the same as model (3).
Model (4) is a nonlinear programming whose objective function contains absolute value. It is hard to solve. To make it easier to solve, two intermediate variables α q and β q are defined, where (4), we can get the equivalent model (5).
In model (5), the objective function of model (4) is converted to a linear function. f q in constraint is replaced byα q − β q + f q0 . e others are the same as model (4).
By solving model (5), we can get α q and β q meeting the requirements of the objective function; therefore, f q � α q − β q + f q0 . At this point, we complete the establishment of the BL-DEA model for carbon trading allowance allocation with the baseline idea introduced:

Selection of Indicators.
ere are many factors that affect the carbon emissions in the road transportation. To ensure the scientific and reasonable selection of indicators, this paper employed Delphi method for survey of experts in the transport industry. Delphi method, as a method for anonymous correspondence to feedback, is widely used in evaluation, forecasting, and determination of influencing factors. Some scholars also used it as a practical tool for statistical work [45,46]. Delphi method was used to conduct two rounds of expert consultation to determine the final input-output indicators.
Before the first round of survey, a preliminary indicator set was established through theoretical analysis, including 2 primary indicators and 10 secondary indicators, as shown in Figure 2. e full mark frequency, grade sum, and coefficient of variation are selected as the basis for indicator screening, which means ① Full mark frequency (P i ): this indicator represents the ratio of the number of experts who are more than general important to the total number of experts. When P i ≤ 50%, it is deemed that the level of importance of the indicator is insufficient and the indicator will be deleted. ② Grade sum (F i ): it is the total score of expert evaluation of an indicator. is paper assigns 0, 1, and 2 to unimportant, general, and important in the first round of expert evaluation. When F i ≤ n, the indicator will be deleted; in the second round of expert evaluation, unimportant, less important, general, relatively important, and important are assigned 0, 1, 2, 3, and 4, respectively. When F i ≤ 2n, the indicator will be deleted.
In the above formula, F i is the grade sum of the no. i indicator; R ij is the value of the no. j expert's score on the no. i indicator. ③ Coefficient of variation (CV i ): it is used to judge whether experts have large differences in the evaluation of indicators. e coefficient of variation (CV) is used for testing. e smaller the value is, the smaller the difference is: where CV i is the coefficient of variation of the no. i indicator; σ i is the standard deviation of the expert score of the no. i indicator; M i is the arithmetic average of the expert score of the no. i indicator.
In the first round of expert surveys, 50 questionnaires were distributed and 42 were recovered, with a recovery rate of 84% and an effective rate of 100%. In the second round of expert surveys, 50 questionnaires were distributed and 40 were recovered, with a recovery rate of 80% and an effective rate of 100%. Information of the two rounds of survey is shown in Table 1.
It can be seen from Table 1 that after the first round of survey, 4 indicators were deleted based on the full mark frequency and grade sum. In the second round of survey, each full mark frequency is greater than 50%, each grade sum is greater than 80, and each coefficient of variation is less than 0.2. It can be considered that after this round of survey, the expert opinions have tended to be unified, and the indicator system can be determined.
To sum up, the number of employees, the number of vehicles, the fuel consumption, and the initial allowances for carbon emission are selected as input indicators under the BL-DEA model. e output value and transportation volume are selected as output indicators.

Emission Intensity Based on CDF.
ere are two main factors that affect the delimitation of the baseline value of carbon intensity in the road transportation. e first is that the selection of a reference indicator can accurately reflect the industry's performance gap in energy conservation and carbon reduction. e second is to confirm the specific situation of the current carbon intensity in the entire industry. In terms of indicator selection, compared with per unit mileage carbon intensity, per unit of passenger and freight turnover can both effectively reflect the carbon intensity of a vehicle and the carbon intensity of a passenger and freight vehicle in transport capacity, which complies with industry characteristics and is in line with existing statistical indicators of the road transport industry. e calculation formula of such indicator is as follows: where c is carbon intensity per unit of passenger and freight turnover in g/t · km or g/p · km; m f is fuel consumption of vehicle (L/100 km); ρ is fuel density: 0.85 kg/L for diesel and 0.75 kg/L for gasoline; Q l is average low calorific value of fuel (kJ/kg); k is potential CO 2 emission coefficient (kg/GJ), according to data released by the National Development and Reform Commission of the P.R.C., and the values are shown in Table 2. W is the rated load or passenger capacity of a vehicle, and the unit is ton or person.

Data Acquisition and Analysis.
e Ministry of Transport of China has started to manage the standards of fuel-based commercial buses and commercial trucks since 2008 and has established a database of highway transport vehicles that meet the standards [47]. Corresponding technical parameters of 2,000 related models from 2016 to 2018 have been obtained through inquiry and can basically  Journal of Advanced Transportation cover the overall application situation of current operating vehicles in the industry. e carbon intensity of existing models is calculated by using formula (8). Figures 3 and 4, respectively, list the scattered points and distribution of carbon intensity of 1,679 truck models and 362 passenger vehicle models for statistical analysis of data.
As can be seen from Figure 3, the current application of commercial trucks in China presents many dense typical models, a wide coverage of rated load, and a large gap in carbon intensity. e rated load range of commercial trucks is about 3 t∼40 t, and the main quality segment is concentrated between 8 t and 20 t, which also shows that there are many truck models in China, and tractor models are concentrated. e carbon intensity per unit of freight turnover ranges from 40 to 190 g/t·km and is most concentrated within the range of 50 to 100 g/t·km. A single payload may have different carbon intensities, and the probably reasons are as follows: firstly, based on the formula (8), the fuel consumption of vehicle has a great influence on carbon emission intensity. Meanwhile, the total mass of the vehicle has a great influence on the fuel consumption. e total mass of the vehicle is composed of vehicle weight and payload. e difference of vehicle weight leads to the difference of carbon emission intensity for the vehicles with the same payload.
erefore, for the vehicles with small payloads, vehicle weight takes a larger proportion in the total mass, resulting in a large difference in carbon emission. For the vehicles with large payloads, vehicle weight takes a small proportion in the total mass, resulting in a small difference in carbon emission. Secondly, the payloads between roughly 33000 and 40000 have a relatively similar range of carbon intensity. e reason is that this part of vehicles is mainly tractor trucks (different from the single trucks on the left in Figure 3). Vehicle weight takes a similar proportion in the total mass, resulting in a similar difference in carbon emission.
It can be seen from Figure 4 that the commercial buses are more concentrated than truck models, and the distribution of rated passenger capacity is even, and the gap in     Journal of Advanced Transportation carbon intensity is large. e rated passenger capacity ranges from 15 to 55 people, and the number of models with each capacity range is relatively average. ere are fewer models with a capacity of more than 55 people. is also indicates that China has a higher degree of standardization in commercial bus models. e carbon intensity per unit of passenger turnover ranges from 5 to 30 g/t·km and is most concentrated within the range of 10 to 15 g/t·km. Based on the above analysis, it can be seen that in terms of carbon intensity per unit of turnover, the entire road transport industry has a large fluctuation range, with an obvious gap. is also proves that by introducing the baseline idea and scientifically delimitating the industry baseline value, the initial allocation of carbon emission quotas can have an effective incentive effect on the road transport industry.

Cumulative Distribution Function of Sample Data.
Carbon emission intensity data is a set of continuous random variables. According to the central limit theorem, variables obey a normal distribution with a mathematical expectation of μand a standard variance of σ 2 . e probability density function is as follows: e probability distribution diagram of carbon emission intensity obtained by using formula (9) is shown in Figures 5  and 6.
As can be seen from Figures 5 and 6, the probability distribution of emission intensity is in good agreement with the normal distribution. We can confirm the cumulative distribution function of emission intensity by the following formula: By using regression analysis and curve fitting in the Minitab software, the cumulative probability density of the carbon intensity of vehicle models in each classification segment is calculated as shown in Figure 7.
It can be seen from Figure 7 that the cumulative probability density curve of the carbon intensity after the fitting of the commercial buses and trucks is close to the original value distribution, which proves that the fitted curve is in good compliance with the actual situation. By integrating the cumulative probability density distribution of the carbon intensity of various types of passenger vehicles and trucks in the road transport industry and selecting the value at 50% of the cumulative probability density as the industry baseline, the baseline value of industry carbon intensity calculated is shown in Table 3.
e baseline of vehicle carbon emission intensity is based on the vehicle model data rather than individual vehicle data. Although the data of 2000 models are selected, they can basically cover all models of operating vehicles in the current industry. Meanwhile, the fuel consumption data of each model is obtained through the full-load test specified in the standard, which can effectively represent the emission intensity level of the vehicle. erefore, the matching between the baseline value and the reality is guaranteed. e purpose of vehicle carbon emission intensity baseline is to encourage the industry to reduce intensity as much as possible. Increasing vehicle payload is an important measure to reduce the intensity. erefore, the baseline is determined based on the full load of the vehicle.      Table 4. Data in columns 2-8 of the table are directly inquired from related statistical yearbooks.

Results and Discussion
Data in the rightmost column are obtained through calculation. e calculation method is as follows: where f q0 is the initial quota allocation value based on the baseline in 10,000 tons; c p is the baseline value of carbon intensity of commercial buses: 13.12 g/p·km; c f is the baseline value of carbon intensity of commercial trucks: 75.04 g/t·km; ε p is passenger turnover in 100 million p·km; and ε f is freight turnover in 100 million t·km. Guangdong's current highway mileage is the longest in the country. Henan, Anhui, Hunan, and Hebei have all obtained more than 30 million tons of quotas. ese four provinces are also the provinces with large highway transport traffic in China. ey are among the best in terms of vehicle ownership, number of practitioners, and fuel consumption. Shanghai and Beijing are two regions in the country allocated with least carbon emission right quotas. e first is that compared with other provinces, the scale of highway transport in these two large cities is still small. e second is that except for highway transport, railways, aviation, and other means of transport in Beijing and Shanghai are relatively developed, which have also reduced the volume of highway transport to a certain extent. In general, through macro analysis, the initial quotas allocation value calculated by using the BL-DEA model can better match the economic development level, the development status of the highway transport industry, and the scale of the highway transport industry in various regions. It is a basic and reasonable allocation method.

Carbon Reduction Potential Analysis of Provinces.
Carbon emission intensity was taken as an important benchmark index in the BL-DEA model. Compared with the actual carbon emissions of 30 provinces, carbon emission quotas by BL-DEA can reflect carbon reduction potential. A comparison is shown in Figure 8. As can be seen from Figure 8, in terms of carbon intensity, 53 percent of provinces have smaller quotas than their actual emissions and 47 percent of provinces have higher quotas than their actual emissions. Shanghai, Guangdong, and Xinjiang have the greatest carbon reduction potential. e carbon emission intensity of these three provinces is at a relatively high level. By improving the carrying capacity of transportation, applying carbon-reducing technologies, and optimizing transportation organization, carbon emission would be significantly reduced. Henan, Hunan, and Anhui have the largest increase in emission quotas. e carbon  Vehicle type Baseline value of carbon intensity Commercial trucks 75.04 g/t·km Commercial buses 13.12 g/p·km emission intensity of these three provinces is at a relatively low level. e most benefit would be obtained when carbon trading market opens.

Comparison and Discussion of Different Quota Allocation
Methods. In order to compare the promotional effect on the development of the industry among the BL-DEA model and the most widely used historical responsibility law and baseline method methods, this paper carries out discussions from three aspects, respectively: efficiency, equity, and incentives. e efficiency of the allocation of initial allowances for carbon emission represents its role in the production and operation efficiency and the healthy development of the entire highway transport industry. e equity represents the difference between the emission quotas of the provinces and the average value of quotas among provinces. Smaller difference indicates that quotas are distributed more evenly among provinces, which can conducive to promotional effect in the industry. at means more equity. e incentive represents whether provinces with lower carbon intensity have certain quota incentives and provinces with higher carbon intensity have certain quotas penalties to promote the enthusiasm of the entire industry for energy conservation and carbon reduction.
In terms of efficiency comparison, the traditional CCR model proposed by Charnes et al. [49] was used. e quotas allocated by "baseline" method have been listed in Table 4. Under the historical responsibility method, quotas are allocated by the percentage of existing carbon emission data; the quotas are shown in Table 6.
It can be seen from Table 7 that under the "historical responsibility" method, Guangdong and Shandong have, respectively, obtained 50.8 million tons and 41.48 million tons of carbon emission right quotas, still ranking top two. e difference is that Guangdong becomes the province with the most allowance. e reason is that highway transport industry of Guangdong has the largest total carbon emissions, so it has been given the most initial allowance. Hainan has become the province with the least allowance in the country. Because Hainan is located on an island and the highway transport within the province cannot go out of the  island, so its industry scale is small and it has become the province with the lowest carbon emissions. In addition, allowances in Ningxia and Qinghai do not exceed 4 million tons, mainly because the two provinces are relatively underdeveloped, with fewer people and freight flows, and the scale of highway transport is not large, resulting in small mileage carbon emission data. e efficiency value based on the CCR method which was recorded as CCR-DEA efficiency is shown in Table 7. Further, changes in the efficiency values of the three allowance allocation methods are shown in Figure 9.
As can be seen from Table 7 and Figure 9, under the distribution model of the historical responsibility method, the CCR-DEA efficiency of 6 provinces including Beijing, Hebei, Anhui, Fujian, Hunan, and Guizhou reaches 1, and the number of such provinces accounts for 20% of all. e efficiency in Qinghai and Xinjiang is relatively poor at only 0. 43  is also proves that in the current two allocation models in common use, the allocation efficiency under the baseline method is relatively higher and can better promote the development of the industry. Under the BL-DEA allocation model, through the adjustment of the provinces under a fixed overall allowance, the efficiency of all provinces has reached 1. is shows that the BL-DEA allocation model is more scientific, as compared with the existing two allocation methods, taking into account the benign development of the industry and the efficiency of production and operation.
In terms of allocation equity, the initial allowances allocated to each province under the three different allocation models are also somewhat different. A comparison of the equity in allowance for carbon emission under three allocation methods is shown in Figure 10.
It can be seen from Figure 10 that quotas of most provinces under the BL-DEA model are between the others. In order to quantitatively compare the equity of the three allocation methods, this paper uses variance to measure the difference between the emission quotas of the provinces and the average value of quotas among provinces. e calculation method of the variance is as follows: where σ 2 is the variance of emission quotas under different allocation methods; X is the values of emission quotas for each province under different allocation methods; μ is the average value of quotas among provinces;N is the number of provinces. After calculation, the variances under the three methods, namely, "historical responsibility," "baseline," and "BL-DEA model," are 1087178, 2386464, and 1376641, respectively. Considering that the incentive effect will inevitably result in loss of equity, the variance under the "baseline" distribution model is the largest. e allocation variance under the BL-DEA model has been significantly reduced compared to the "baseline" method and has been slightly increased compared to the "historical responsibility" method. is indicates that the model can better achieve equity while ensuring efficiency and incentives and is more conducive to the implementation of the carbon trading system in the entire highway transport industry.
It can effectively increase the enthusiasm of enterprises participating carbon trading in energy conservation and carbon reduction by reflecting the incentive effect in the allocation of initial allowances for carbon emission to various provinces. is will greatly promote the achievement of the national carbon emission reduction goal. erefore, this is also an important factor in evaluating allocation models. A comparison of carbon emission incentives under the three allocation models is shown in Figure 11.
It can be seen from Figure 11 that the allocation trends of three allowance allocation methods of initial allowances for all provinces are roughly the same, but there are still some differences among different provinces. Compared with the Table 6: Allocation of quotas based on the "historical responsibility" method.
"historical responsibility method," in terms of incentives, under the BL-DEA allocation model, Shandong and Guangdong still occupy the top two places in allowance allocation, but Guangdong has dropped from the first place under the "historical responsibility method" to the second place. is is mainly attributable to the relatively high carbon intensity per unit of traffic volume in Guangdong's highway transport industry.
e allowances under the BL-DEA model are reduced as compared with the initial allowances, which clearly reflect the incentive effect of the BL-DEA  developed regions and led to general and certain increase in the allowances allocated under the BL-DEA to central and western regions such as Henan, Hunan, Guizhou, and Shanxi. Compared with the "baseline method," the quotas under the BL-DEA model to Hebei Province have decreased by 33.1 million tons. Hebei is located on the plains and is China's largest province for freight transport. Freight transport is mainly long-distance transport and drop and pull transport (a motor vehicle drops the loading device attached to the vehicle at the destination and then pulls other loaded devices back to the original place or a new location). Freight mileage is nearly three times that of Guangdong, and the actual load rate is relatively high. is has caused Hebei's carbon intensity per unit of freight turnover to be significantly lower than the industry average. erefore, the "baseline method," which uses incentives as its main indicator, gives large allowances. However, under the BL-DEA model, in order to consider efficiency and equity as a whole, allowances allocated to Hebei have been greatly reduced. For allowances allocated to other provinces, the allowances allocated under the BL-DEA model fluctuate to some extent based on the allowances allocated under the "baseline method," but the fluctuation is not great.
is proves that the allowances under the model significantly approximate those under the "'baseline method" and such model can effectively reflect the effect of incentives.
Based on the above analysis, it can be seen that BL-DEA, as a comprehensive initial allowance allocation model, has greater growth in allocation efficiency than the other two models, as compared with the current "historical responsibility method" and the "baseline method" that are most widely used, with the comprehensive allocation efficiency increasing by 19% and 14%, respectively. In terms of allocation equity, compared with the "baseline method," it can better balance equity and has little difference from the "historical responsibility method." In terms of allocation incentive effect, compared with the "historical responsibility method," the incentive effect is obvious. Compared with the "baseline method," except for Hebei, the allocation incentive effect to other provinces has reached a relatively high level.

Conclusion
is paper establishes an improved initial allowance allocation model from the perspective of carbon emission intensity, which can be applied to the road transportation. Initial quotas are allocated to 30 provinces and regions in China by the use of the proposed model. e conclusion is as follows: (1) e carbon emission intensity of commercial trucks and buses in China's road transport industry is 75.04 g/t·km and 13.12 g/p·km, respectively. (2) In terms of carbon emission reduction potential, 53 percent of provinces have smaller quotas than their actual emissions; 47 percent of provinces have higher quotas than their actual emissions; Shanghai, Guangdong, and Xinjiang have the greatest carbon reduction potential; Henan, Hunan, and Anhui have the largest increases in emission quotas. (3) In terms of allocation efficiency, the proportion of provinces with an allocation efficiency of 1 increases from 20% under the "history responsibility" method and 27% under the "baseline" method to 100%. e comprehensive average allocation efficiency increases from 0.81 under the "historical responsibility" method and from 0.86 under the "baseline" method, to 1, increasing by 19% and 14%, respectively. (4) e proposed model comprehensively considers the incentive effect brought by the high and low unit carbon intensity across provinces and local economic development level. In terms of allocation equity, the allocation variance under the BL-DEA model declines significantly as compared with that under the "baseline method" and increases slightly as compared with that under the "historical responsibility." Due to the limitations of the study, there are still some areas in this paper that need improvement in future research. e first is that the data used in this paper are the current base year data. e current data are utilized to clarify the validity of the BL-DEA model in the allocation of initial allowances for carbon emission. In future work, the carbon emission forecast shall be carried out according to the economic development level in China and the transport development level in various regions, and then, an allowance allocation study shall be conducted for the target year based on the forecast. e second is that this study only focuses on traditional fuel vehicles rather than new energy vehicles, due to the fact that the current application of new energy vehicles in the road transport industry has not yet formed a scale. With the increasing new energy vehicles, in future research, efforts shall be made to explore the impact on the allocation of initial allowances for carbon emission after an enterprise uses new energy vehicles.
Data Availability e input-output indicator data of road transportation used to support the findings are included within the article. e data of carbon emission intensity used to support the findings have been deposited in the Figshare repository (https://doi.org/10.6084/m9.figshare.12291248.v1). e database contains the carbon emission intensity of the unit turnover of passenger and cargo vehicles in China, which can be used to calculate the carbon emission intensity baseline of the road transportation.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper. 16 Journal of Advanced Transportation