Green Innovation Efficiency Measurement Model for the Logistics Industry

(1) Measurement methods

The GIE of China's logistics sector is assessed in this study using the SBM super-efficiency mode [53]. The dynamic changes in GIE within this industry are investigated through the application of the MI index approach.

While DEA is a widely accepted approach for efficiency measurement, traditional DEA models face challenges in addressing slackness in output and input factors, potentially compromising efficiency accuracy [54]. To overcome these limitations, the SBM super-efficiency model, introduced by Tone [55], is chosen for its capacity to simultaneously consider inputs, desired outputs, and undesired outputs. This model has gained popularity across various fields for its comprehensive analysis capabilities. Accordingly, the article adopts the SBM for assessing the GIE of China's logistics sector. The model's formula is outlined below:

The efficiency value is represented by ρ_SE, with x and y indicating the input and output elements, respectively. The model includes m input indicators and s output indicators, with i and j representing the decision-making units for inputs and outputs S⁺ and S⁻ denote the input and output slack, respectively. r_j denotes the vector of weights.

Additionally, the study applies Malmquist index (MI) analysis to track the evolution of total factor productivity, focusing on addressing undesired output [56]. The MI is grounded in DEA models, and the core of the MI is to solve the problem of undesired output [54, 57]. Therefore, this study applied the MI analysis to analyze the dynamic variations in GIE in the Chinese logistics industry. This involves defining a directional distance function and constructing a global total factor productivity (MI) by integrating GIE measures specific to the logistics sector.

In the formula, E^g,t(x^t, y^t, z^t) denotes the global efficiency value in period t, E^g,t+1(x^t+1, y^t+1, z^t+1) denotes the global efficiency value in period t + 1, and MI^t,t+1 denotes the total factor productivity index from period t to t + 1.

(2) Measurement indicators

The analysis categorizes GIE indicators into inputs and results measures. Input signals encompass investment expenditure [42], labor input [58], and energy input [4, 59]. Labor input is measured by the workforce size in transportation, storage, and postal services, while energy input is gauged by the sector's energy used by the industry. Because it is difficult to obtain direct data from Chinese yearbooks, the logistics sector's capital stock— which is determined using the "perpetual inventory method"—infers capital input, which is impossible to assess directly.

Where Κ_i,t and Κ_i,t-1 denote the capital stock of city i in year t and t − 1, respectively, I_i,t is the amount of fixed asset investment in city i in year t, and δ denotes the depreciation rate of fixed assets. After choosing a defined base period, the above equation is transformed by iteration, and its formula is as follows:

In Equation (5), it is critical to calculate the investment amount, base period stock, and the economic depreciation rate for year i. For the investment amount in year i, considering the references from prior research and data availability, this study chooses the fixed asset investment as the reference data. For determining the base period stock, this research refers to the initial stock proposed by Reindorf (2005), calculated using the following formula:

I₀ signifies the constant price investment during the base period, g stands for the average annual growth rate under constant price investment, δ indicates the average capital depreciation rate (the growth rate of fixed asset investment in each province and city for the year 2006 was used for the 30 provinces and cities to determine this value) and the economic depreciation rate was calculated using a formula with a value of 9.6% [60].

Output metrics are categorized into desired and undesired outputs. Desired outputs are measured by freight turnover [58], the number of patents granted in the logistics sector [61], and the industry's value added; carbon dioxide emissions [3, 62] are identified as the undesired output, with fossil energy consumption used to estimate the carbon footprint of the logistics sector across 30 cities and provinces in China, calculated by the formula:

E_i is the total consumption of energy source i, NCV_i is the average low level heating value of energy source i, CEF_i is the carbon emission factor of energy source i, and COF_i is the carbon oxidation factor.

The details of the variables that are entering and leaving to assess the efficiency of green innovation in China's logistics industry are presented in Table 1.

Spatial Effect Measurement Model of Green Innovation Efficiency in the Logistics Industry

The spatial network structure of GIE in China's logistics industry is examined in this study using social network analysis, and the position and function of every municipality and province within the spatial network are analyzed using the plate model.

(1) Social Network Structure

Social network analysis is utilized to depict cooperative relationships among nodes in urban network studies [63]. This study uses network density, network efficiency, and the degree of network level in social network analysis to explore the overall network characteristics of 30 provinces and cities, and employs point centrality, betweenness centrality, and closeness centrality to investigate the individual network features.

(2) Modified Gravity Model

Prior to conducting a social network study, a spatially related matrix is created. This is usually done by measuring the relationship strength and inherent connection mechanism of the spatial network connecting cities using the gravity model found in the literature [14]. The geographic relationship strength of innovative green efficiency in the logistics sector across 30 Chinese provinces and cities is measured in this study using a modified gravity model. The spatial relationship matrix is created using the following formula:

where S is the intensity of the spatial linkage of GIE in the logistics industry; E_i and E_j denote the GIE of the logistics industry in regions i and j, respectively; D_ij denotes the distance between regions i and j, with specific data derived from ArcGIS software; G_i and G_j denote the total GDP of regions i and j, respectively; and g_i and g_j denote the gross regional product of regions i and j, respectively.

The values of linkage strength less than 100 are hidden due to the large extreme difference in the strength of the association measured by the modified gravity model; therefore, linkage strength greater than 100 is divided into four stages: the first stage, the second stage, the third stage, and the fourth stage.

(3) Overall Network Architecture

Network density reflects the compactness of a spatial network's structure. A higher network density indicates more interconnected nodes and a greater influence of resource flow within the network on individual nodes [64, 65]. In this study, network density is quantified by comparing the actual number of links within the network to the maximum possible connections across the entire network. This ratio, which falls between 0 and 1, is calculated as follows:

where n denotes the number of cities and n×(n − 1) is the maximum number of possible correlations.

Network efficiency is defined by the number of superfluous connections in a network relative to a specific number of network members [66]. A lower network efficiency value suggests an increase in spillover channels among node cities, thereby stabilizing the network trend. The network efficiency calculation formula is

where Κ is the number of excess lines, and max(K) is the maximum possible number of excess lines.

The network hierarchy indicates the rank of each node city or province within the network, denoting their importance and influence. A higher degree of network hierarchy enhances network accessibility and signifies a more stratified network structure. It is determined by the following formula:

where M denotes the number of symmetrically reachable member pairs in the network and max(M) denotes the maximum possible number of symmetrically reachable member pairs.

(4) Individual Network Structure

Point degree centrality refers to the radiation and absorption capacity of a node, province, or city within a network. The number of direct links between nodes is how it is expressed. Point-degree centrality can be further classified into point-in and point-out. Point-in represents the number of connections accessing a node, province, or city, indicating the extent to which it is influenced by other nodes in the network. On the other hand, point-out denotes the number of relationships sent out, indicating the ability of the node, province, or city to impact other nodes [66].

The degree of intermediary centrality characterizes the node's, province's, or city's ability to control and regulate each resource in the network [14]. This is calculated using the following formula:

where g_ij is the number of associations that exist between regions i and j and g_ij(i) is the number of paths between i and j going through i

Proximity centrality measures the minimum distance between two cities or provinces, indicating the ease of resource transfer between provinces and municipalities [7]. It is determined by the following formula:

where d_ij is the straight-line distance between province and city i and province and city j is indicated.

(2) Plate Model

Plate modeling is a widely utilized method for analyzing spatial network structures through spatial clustering. It is crucial to clearly define the interconnections among locations within the plate structure during plate modeling [67]. These relationships can appear in four distinct forms. The first is the bilateral spillover plate, characterized by its dual role in both sending and receiving interactions with other plates, alongside maintaining numerous internal relationships. The second type is the main beneficiary sector, where the plate predominantly receives interactions, both internally and externally, rather than contributing spillover to other plates. The third form is the main overflow board, notable for its tendency to create more outgoing connections than it receives. The fourth type is the broker board, unique in its balance of incoming and outgoing links with a limited number of internal connections. This categorization led to the identification of four distinct segments, as detailed in Table 2.

Table 2 posits that block G_k includes city g_k, the total number of potential relationships G_k within block is g_k(g_k − 1). Given that the spatial association network includes g cities; therefore, the number of possible relationships G_k in each block city is g_k(g − 1) in the spatial association network, and the expected internal relationship ratio is g_k(g_k − 1)/g_k(g − 1) − (g_k − 1)/(g − 1) .

Logistics Green Innovation Efficiency Drivers Identification Model

(1) Measurement methods

The elements impacting the spatial network structure of GIE in the Chinese logistics sector are examined in this study using QAP analysis. QAP, a matrix algebra-based method, is adept at assessing the similarity and correlation between two matrices [68].

The QAP correlation analysis involves initially randomizing the relation matrix, then comparing the similarity between the two matrices, determining the number of relations, and conducting non-parametric testing. The process entails: 1) treating all matrix values as vectors to compute the relationship coefficient between both vectors, 2) randomly replacing one matrix, shuffling all its rows and columns, followed by computing and saving the relationship coefficients between the altered matrix and the original, 3) analyzing the distribution of correlation coefficients post-replacement to conduct QAP correlation.

QAP regression goes deeper, analyzing and assessing the importance of the correlations between individual matrices and many matrices. It includes 1) conducting multiple regression analyses on all independent variable matrices against the elements of the dependent variable matrix, and 2) recalculating the regression after randomly rearranging the dependent variable matrix's rows and columns storing all of the obtained coefficient values.

(2) Measurement indicators

This study analyzes six dimensions: spatial proximity, extent of opening to the outside world, industrial structure, level of urbanization, degree of technological and scientific advancement, , and energy intensity. These dimensions are based on relevant studies by scholars [2, 39, 69]. The spatial matrix of innovative green efficiency in the logistics sector serves as an explanatory variable for data processing. The values of the indicators are represented as difference matrices, detailed in Table 3.

Overall Network Structure

This study examines the spatial network framework of innovative green efficiency in the Chinese logistics sector, treating each province and city as a network node and analyzing the connection strengths between them using ArcGIS tools. The results, illustrated in Fig. 4, reveal a considerable variance in the spatial network structure across the 30 provinces and cities studied. The overall spatial network displays an imbalanced distribution, with the eastern and central regions having lower levels of innovative green efficiency and the western regions having greater levels. The eastern region's network is anchored by the initial and second levels, while in the central region, the 3rd and 4th order links rely on a minimal presence of initial and second order links. The western region is characterized by a predominance of third and fourth level links, albeit with fewer connections overall. The majority of China's most connected provinces and cities are found in the country's east and center, while the majority of its least connected provinces and cities are found in the country's center and west, particularly in Xinjiang, Qinghai, and Ningxia.

Fig. 5 displays the results of the study's computation of the network density, network efficiency, and network hierarchy of the spatial connection of innovative green efficiency in the logistics sector. It was observed that the network density increased gradually over the study period, peaking in 2021. In contrast, the overall network efficiency showed a declining tendency, with the highest efficiency recorded in 2012 and the lowest in 2021, averaging 0.623. Similarly, the network hierarchy decreased over time, with an average value of 0.1208.

Individual Network Structure

The spatial distribution of the point-entry degree in the GIE network within the logistics sector among 30 Chinese municipalities and provinces for the years 2012, 2017, and 2021 is depicted in Fig. 6. The areas with higher point-entry degrees are predominantly located in the eastern region. In 2012, Tianjin and Shanghai led the first tier, followed by Beijing, Jiangsu, and Guizhou in the second tier. Between 2012 and 2017, Beijing ascended to the first tier, with Fujian and Zhejiang provinces advancing to the second-highest value area. From 2017 to 2021, the second tier expanded westward around the first tier. Xinjiang consistently remained in the low-value tier, and in 2021, Qinghai Province moved up from the fourth to the third tier.

For the same set of cities and provinces in the same years, Fig. 7 shows the spatial distribution of the point-out degree in the GIE network. In 2012, the first tier included Tianjin, Jiangsu, Shanghai, and Beijing, while the second tier comprised Shandong and Zhejiang provinces. From 2012 to 2017, the first tier expanded, and the second tier spread southward, forming a cluster with Shandong, Jiangsu, Shanghai, Zhejiang, Fujian, Guangdong provinces, and Beijing and Tianjin municipalities as localized central hubs. Between 2017 and 2021, the first tier continued to grow, with Hubei Province and Chongqing Municipality rising to this tier, and several provinces moving from the third to the second tier. The fourth tier was mainly in western China.

Fig. 4.

Spatial correlation network of innovative green efficiency in the logistics industry.

Fig. 5.

Network correlation of innovative green efficiency in the logistics sector from 2012 to 2021.

The analysis of both point-in and point-out degrees reveals a consistent correlation between the two, i.e., the high and low point-in rankings of provinces and cities are consistent with point-out. This indicates that there is a bidirectional link in innovative green efficiency within the logistics sector. Higher degrees in both metrics are typically associated with more sophisticated logistics in provinces and cities.

Fig. 8 displays the spatial distribution of the GIE network's mediating centrality degree. In 2012, Beijing, Tianjin, and Shanghai were in the first tier. By 2017, Jiangsu Province had moved up to the first tier, with Zhejiang and Fujian provinces advancing to the second tier and Jiangxi Province dropping to the third tier. By 2021, there was a general decline in mediating centrality values across most provinces and cities, with Hunan, Guizhou, and Guangxi falling to the fourth tier and diminishing their role as network bridges.

Fig. 6.

Spatial distribution of point penetration of an innovative green efficiency spatial connection network in the logistics industry.

Fig. 7.

Spatial distribution of an innovative green efficiency spatial connection network in the logistics industry.

Fig. 8.

Spatial distribution of the mediated centrality of spatially relevant networks for green innovation efficiency in the logistics industry.

Fig. 9 shows the spatial distribution of proximity centrality from 2012 to 2021. Initially, the first tier included Tianjin and Shanghai, with Beijing and Guizhou in the second tier. By 2017, proximity centrality values had significantly increased across all regions, with all provinces and municipalities in the third tier or higher. In 2021, the trend continued, with Heilongjiang, Xinjiang, and Qinghai in the third tier, and the rest in the second tier or higher. The first tier mainly consists of economically advanced provinces and cities, which form the core of the network and can quickly establish connections with others, while the second tier includes peripheral regions, where geographical factors may limit interaction and depend on the development of central areas.

Plate Structure Analysis

These 30 cities are categorized into four segments, with the cities in each segment listed in Table 5. The spatial linkages and spillover effects among these segments are detailed in Table 9.

Table 6 reveals that out of 456 spatial correlations, 52 are within segments and 404 are between segments, accounting for 88.6% of inter-segment correlations. For the first segment, it receives 17 internal and 128 external relationships, with 113 spillovers coming from outside the segment. The anticipated internal relations ratio was 37.93%, but the actual figure was only 13.08%, indicating prevalent "two-way spillovers." In the second segment, there are 103 outside and 15 inner receiving relationships, with 60 spillovers from outside, leading to an actual internal relations ratio of 20% against a forecasted 27.59%, marking it as the "primary beneficiary effect." The third segment shows 15 internal and 95 external receiving relationships, with 150 external spillovers. Its internal relational rate was expected to be 17.24% but turned out to be 9.09%, classifying it as a "major spillover effect" area. The fourth segment has 5 internal and 78 external receiving relationships, with 81 external spillovers. Its internal relations ratio, projected at 6.9%, was actually 5.81%, making this segment a broker segment.

The density matrix between the segments is computed in this study in order to further investigate the correlation. The multivalued density is also converted into an image matrix. Taking the average spatial association network density of the study object, 0.4897, as a benchmark, values in the network density matrix greater than 0.4897 indicate a density level above the overall network level, denoted as 1; otherwise, it is denoted as 0. The distribution of GIE spillovers is demonstrated by the results, which are displayed in Table 7. In the density matrix, the magnitude and intensity of spillover impacts are directly correlated. The findings indicate spillovers from the first segment primarily affect the third and fourth segments. The second segment's spillover effects mainly impact the fourth segment, while the third and fourth segments influence all segments. In the image matrix, the first segment is a bi-directional spillover segment with a value of 1 with the third and fourth segments and a value of 0 with the others. The second segment, identified as the main beneficiary segment, has a value of 1 only with the fourth segment. Both the third and fourth segments have a value of 1 for all segments.

Fig. 9.

The spatial relationship network of green innovation efficiency in the logistics industry is close to the spatial distribution of centrality.

The internal relationships between the various innovative green efficiency segments in the Chinese logistics sector are depicted in Fig. 10. The foremost segment acts as the primary driver of innovative green efficiency, while the fourth segment serves as a pivotal bridge in the transmission mechanism, highlighting a pronounced disparity between the GIE segments of the logistics sector.