Efficiency Evaluation of Logistics Industry in the Beijing-Tianjin-Hebei Region under Low-Carbon Constraints Based on the DEA-Malmquist Model

This paper studies the logistics efficiency of the Beijing-Tianjin-Hebei region under the background of low-carbon economy from 2012 to 2017. We introduce the carbon dioxide emission into the input indicators on the basis of the pollutant input method, and we use the BCC model and Malmquist index model to make both static and dynamic efficiency evaluations of logistics industry. Also, we use the projection analysis method to analyze the root causes of DMUs with non-DEA efficiency. According to the problems of logistics efficiency in Beijing-Tianjin-Hebei region, we put forward some recommendations to help the whole region achieve collaborative development under the low-carbon environment.


Introduction
The Beijing-Tianjin-Hebei region is China's "capital economic circle" and the region with the largest economy scale and the greatest development potential in northern China. As the accelerator of economic development, logistics industry provides strategic industrial support for economic development, and its efficiency is often used to evaluate the development level of a country or a region1. Data Envelopment Analysis (DEA) is a method of relative efficiency evaluation using multiple homogeneous decision-making units (DMUs), and it is widely used in logistics efficiency evaluation. Zhang  Under the trend of low-carbon economy, logistics industry, as a large energy consumption and carbon emission industry, has become the key industry of energy conservation and emission reduction. In current researches, there have been some scholars taking CO 2 emissions into account. Deng et al. (2020) used the SBM-DEA model to analyze logistics efficiency of 30 provinces in China under low carbon constraint1; Guo et al. (2018) used the DEA-BCC model to calculate the logistics efficiency in the Beijing-Tianjin-Hebei region and used the projection analysis to analyze the non-DEA effective DMUs4.
At present, there are few studies of logistics efficiency in the Beijing-Tianjin-Hebei region considering CO 2 emissions. Based on the current researches, this paper introduces CO 2 emissions of logistics industry into the input indicators and analyzes both static and dynamic efficiency by the BCC model and Malmquist index model. In addition, this paper uses the projection analysis method to analyze the factors that affect logistics efficiency, so as to promote more suitable recommendations for the development of logistics industry in the Beijing-Tianjin-Hebei region. . .
In the basic BCC model, DMUs can be regarded as the process of generating a certain amount of outputs with a certain amount of inputs under particular circumstances. For region j, DMU (j = 1,2, ..., n) has m input indicators and s output indicators. and represent the numerical value of the ℎ input indicator and the ℎ output indicator of DMU (i=1, 2,..., m; r= 1, 2,..., s) respectively.
denotes the weights of the input-output indicators; and are the respective slacks for the input and output variables, and is the non-Archimedes infinitesimal. If 1, 0 , it is the optimal solution, suggesting that it reaches the DEA frontier and the TE equal to 1; if 1, 0 or 0 , it indicates the weak efficiency; when 1 , it is inefficient, and in order to achieve the optimal technical efficiency, it is necessary to analyze the projection of DEA invalid units and make some adjustments for input and output values.

Projection analysis
For DMU with the value of TE less than 1, the projection analysis can help to calculate the improvement direction of the DEA invalid area. Set * ; * , and * , * is the projection of the efficiency frontier for , .Then, the input redundancy ∆ and the output inadequacy ∆ can be expressed as:

Malmquist index model
The Malmquist index model is proposed by Sten Malmquist, a Swedish economist and statistician, in 1953. Based on Sten's research, Caves et al. (1982) introduced the distance function, which reflects the Total Factor Productivity change (TFPCH) through measuring the distance between the DMU and the production frontier6. Fare et al. (1992) further applied it to the study of production efficiency and combined the non-parametric linear programming method with DEA theory to construct the Total Factor Productivity Malmquist index7. In order to avoid the randomness of time selection, the geometric mean of and is chosen to calculate the Malmquist index. Therefore, the Malmquist index, which measures the TFP from to 1, can be expressed as: If M > 1, the productivity increases from to 1; if M = 1, the productivity remains unchanged; if M < 1, the productivity decreases.
The Malmquist total production efficiency change (TFPCH) can be decomposed into the technical efficiency change (EFFCH) and the technology change (TECHCH), from which the key factor affecting the change of Malmquist index can be found. The technical efficiency change is: , , 5 The technology change is: , , TECHCH can be further decomposed into pure technical efficiency change (PECH) and scale efficiency change (SECH), 7 If EFFCH > 1, it indicates that the technical efficiency improves; otherwise, the technical efficiency declines. TECHCH > 1 indicates the technology progress, and the production frontier moves forward. To sum up, Malmquist index is as follows: 8

Indicator selection
In this paper, the logistics efficiency evaluation takes the low carbon constraints into consideration, so we introduce CO 2 emissions into the input indicators based on the pollutant input method. In addition, we choose the number of logistics employees (x 1 ), length of logistics network (x 2 ) and investment in fixed asset of logistics industry (x 3 ) to represent the investment in manpower, material resources and financial resources of logistics industry respectively. Together with CO 2 emission (x 4 ), they compose the input indicators for logistics efficiency evaluation in the Beijing-Tianjin-Hebei region.
In terms of output indicators, considering the economic and social benefits, we choose gross product (y 1 ), cargo volume (y 2 ) and cargo turnover (y 3 ) of logistics industry as output indicators.

Data source
This paper chooses data of input and output indicators in the Beijing-Tianjin-Hebei region from 2012 to 2017, and the data is from China Statistical Yearbook and China Energy Statistical Yearbook from 2013 to 2018. In addition, there is no classification of the "logistics industry" in China's current industrial classification system, so most domestic scholars define logistics as the transportation industry, warehousing industry and postal industry. We choose the same definition in this paper, using the data from transportation, warehousing and postal industries to replace the data of logistics industry. The data of CO 2 emissions can't be gained from the yearbook directly, so we use the calculation method published on the IPCC national greenhouse gas listing guidelines (2006). The fossil fuels that be considered in this paper include raw coal, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, natural gas and liquefied natural gas. By multiplying the consumption of these fossil fuels by their corresponding CO 2 emission coefficient together, we can get the data of CO 2 emissions.
The number of input and output indicators is 7 and the number of DMU is 24, so it meets the DEA empirical rule, which says that the number of DMUs should be two times more than the number of input and output indicators, proposed by Banker et al8. Then, we can do the further research.

Empirical analysis
This paper analyzes the efficiency of logistics industry in Beijing, Tianjin, Hebei and the entire region from 2012 to 2017 statically and dynamically. First of all, we use the BCC model to make a static analysis for logistics efficiency and compare the differences of these DMUs' TE, PTE and SE. Then, we use the projection analysis to explain why some DMUs are non-DEA efficiency. Finally, we use Malmquist index model to make a dynamic analysis in the six years, from which we obtain the TFPCH and its decomposition for each year and each region to make further analysis.

Static efficiency evaluation based on BCC model
According to the input and output data in Beijing, Tianjin, and Hebei province, with the help of DEAP 2.1, we obtain the results of TE, PTE and SE of logistics industry under the VRS condition. Results are showing on Tables 1 and  Table 2.  the other years it also exceeds 0.9. It indicates that the level of technology and management develops well in the entire Beijing-Tianjin-Hebei region, and the logistics scale and the mismatch between logistics input and output are the key factors that restrict the development of logistics industry. In terms of return to scale, the entire region has been in the diminishing stage in the past six years, which shows that this region has structural contradictions in logistics industry. Thus, it is no longer possible to promote the development of the overall logistics industry in the Beijing-Tianjin-Hebei region through expanding the scale of logistics industry.

Projection analysis of non-DEA efficient DMUs
Through the projection analysis, we further explore the input redundancy of the DMUs with non-DEA efficiency in Beijing, Tianjin and Hebei and analyze the reasons why they are inefficient. The results of input redundancy magnitude of non-DEA DMUs are shown in Table 3. There are 15 DMUs in Table 3 in total. In 2012, the redundant magnitude of logistics employees in Beijing is 0.73 and the redundant magnitude of CO 2 emissions is 0.5. Combined with the other years, we can find that the employees and CO 2 emissions redundant are the main reasons for the low TE in Beijing. The reason for non-DEA efficiency in Tianjin is different from Beijing. In 2015, the input redundancy in Tianjin is mainly the inefficient use of fixed asset investments in logistics industry, resulting in waste of resources, while in 2016 it is the excessive CO 2 emissions. As far as the entire Beijing-Tianjin-Hebei region, the main causes of DEA ineffectiveness from 2014 to 2016 are the excessive number of logistics employees and excessive CO 2 emissions, and the length of logistics network had the minimum effect on logistics efficiency.

Dynamic efficiency evaluation based on Malmquist index
According to relevant data and using DEAP 2.1, the Malmquist index of the logistics industry and its decomposition are obtained, showing in Table 4 and Table  5.

TFP analysis of logistics industry in each year.
It can be seen from Table 5

TFP analysis of logistics industry in each region.
Based on the regional differences, we further analyze the efficiency of logistics industry in Beijing, Tianjin and Hebei, and the results are shown in Table 5 Tianjin-Hebei region, the TECHCH only increases by 0.9% in the six years, which shows that it is necessary to enhance technology innovation and promote further development for the logistics industry.

5.2.1
Developing multimodal transport and enhancing the coordinated development in the Beijing-Tianjin-Hebei region. From the above analysis, it can be seen that the logistics comprehensive efficiency in Beijing, Tianjin and Hebei developed well, but for the entire region is not optimistic. This shows that the Beijing-Tianjin-Hebei region lacks effective coordination, and it fails to form an organic whole with complementary advantages and cooperation. Besides, there is too much redundant input, which results in unnecessary waste. The aviation logistics of Beijing, waterway logistics of Tianjin and highway transportation of Hebei are more advantageous, but they are poorly coordinated and connected10. In the future, the Beijing-Tianjin-Hebei region should organically combine these transportation modes to realize advantageous complementarities and promote common development.

5.2.2
Optimizing the structure of logistics employees and cultivating multi-level logistics talents. The advantage of Beijing in technology, culture and talent policy should be made good use of to attract high-end talents in logistics industry and to improve the level of science and technology innovation. Relatively speaking, the ability to attract high-end logistics talents in Tianjin and Hebei Province is deficient. In order to promote the technical capacity of logistics industry, Tianjin and Hebei should improve the welfare treatment for talents, so as to attract more high-end talents. At the same time, Beijing, Tianjin and Hebei should promote technology and information sharing through high-end talents joint cultivation and rational flow, as well as the construction of information sharing platform, to improve the level of science and technology and talent quality in the entire region.

Adjusting the energy structure and turning to low-carbon logistics.
With the rapid development of economy, the demand for logistics business increases. At the same time, energy consumption and CO 2 emission of logistics industry also increase with the scale expansion of logistics industry. This problem is mainly due to the insufficient investment in clean technology and equipment of logistics operations and the backward development of circular logistics and reverse logistics11. Therefore, China should make effort to develop the technology of lowcarbon energy and technology of energy-saving and emission-reducing, to update the logistics equipment with high energy consumption, to promote the use of new trucks with low fuel consumption, and finally, to create a good environment for low-carbon logistics.