Factors Affecting the Evolution of Technical Cooperation among “Belt and Road Initiative” Countries Based on TERGMs and ERGMs

Abstract

The Belt and Road Initiative (B&R), was initiated by China in 2013, and it covers over 60% and 30% of the world’s population and GDP, respectively. The initiative has directed a great deal of investment in energy, transportation, and 5G. Whilst much attention has been focused on cooperation in international trade, technological cooperation in the form of patents has been largely ignored. This paper investigates the formation of technological cooperative relationships among B&R countries within a technical cooperation network. Comprehensive consideration of various factors between participating countries was undertaken, using statistical methods from social network analysis theory. The node attributes and relations between countries and the network structure were studied in a sequence of network analyses using temporal exponential random graph models (TERGMs) and static exponential random graph models (ERGMs). The main findings suggest that research ability, financial ability, technological innovation ability, technological spillover proximity, geographical proximity, and technical proximity have an impact on participation in technical cooperation between B&R countries. Research ability, technological spillover proximity, geographical proximity, and technical proximity have a positive influence on the development of cooperation. However, the financial and technological innovation ability of a country does not actively promote the development of cooperation. The entire cooperation network structure does not have a greater aggregation effect compared with a random network, and intermediary multi-path cooperation is not obvious. This paper analyzes the driving factors for technological cooperation through a systematic study of the characteristics and relationships of B&R countries, and also of the network characteristics among B&R countries. The results of our analysis show that the characteristics of technical cooperation in the B&R region provide a reference for the study of international technical cooperation.

1. Introduction

With the development of economic globalization, technical cooperation is more important than ever. Technical cooperation is a process of continuous information exchange and knowledge fusion between two parties, which can produce a spillover effect of 1 + 1 > 2 and promote the scientific as well as the technological development of both parties [1,2]. In the cooperation process, technical information spreads through personnel, creating a cooperation network which is composed of cooperation nodes and connections through which knowledge flows [3]. The formation of a network is influenced by node attributes, such as the innovation capacity, absorption capacity, and activity level of the nodes [4]. It is also affected by other multidimensional cooperation factors [5], and the interaction between these different factors eventually forms the network. Therefore, researching the factors influencing the formation of a cooperation network can explain the reasons for the current status of technical cooperation [6], improve existing cooperative relationships by strengthening important individual factors, and assist in the establishment of future cooperative relationships [7].

In 2013, China proposed the “Belt and Road Initiative” (B&R), an international cooperation initiative. As early as the Han Dynasty in China, Zhang Qian led an Eastern civilization mission and opened the East–West trade exchange channel. For thousands of years, there has been continuous cooperation between the Eurasian continents. In 2014, the Belt and Road Initiative was upgraded to a national strategy at the work conference of various ministries and commissions. In 2015, these ministries and commissions jointly promulgated the “Vision and Actions on Jointly Building the Silk Road Economic Belt and 21st Century Maritime Silk Road” (the “Vision”), which proposed an overall program and policy guidance. The Vision focuses on policy coordination, connectivity of infrastructure, unimpeded trade, financial integration, and closer people-to-people ties, whereby these closer ties will strengthen scientific and technological cooperation, strengthen multilateral cooperation mechanisms, and promote exchanges between scientific research scholars of B&R countries. In 2016, The Special Plan on Advancing Cooperation of Science and Technology in the Belt and Road Construction was released, which pointed out that the initiative should meet the technological needs of various countries, respect their respective national development strategies, and promote common technological cooperation. In 2019, The Future Outlook of the “Belt and Road Initiative” was released, which also proposed to gather innovation resources from various countries, strengthen scientific and technological cooperation, and deepen a long-term and stable scientific and technological innovation cooperation mechanism. In the same year, at the second Belt and Road Forum on International Cooperation, the participating countries jointly signed the “Innovation Cooperation Initiative”, affirming the foundation of prior technical cooperation, proposing the establishment of a sustainable cooperation model, and strengthening the dialogue mechanism between countries.

The Belt and Road Initiative is a new model of international technical cooperation. Since the turn of the 21st century, science and technology have entered a new era, and emerging industries such as biology, aerospace, artificial intelligence, and telecommunications have developed. The world pattern has changed from there being one or more dominant countries to a more globalized and regionalized pattern [1,8]. Developing countries face new opportunities and new challenges. In terms of scientific and technological development, it is difficult to achieve “one country innovation”; the most realistic choice is to cooperate with other countries. To this end, the dialogue mechanism between countries is constantly improving, and the common regional system ensures basic trust in technical cooperation and the predictability of results. The timely proposal of the Belt and Road Initiative has prompted countries to resolve some cultural and institutional differences, creating a foundation for technical cooperation that has allowed for the formation of a collective consensus under the influence of the common initiative and with a composite of common goals. At the same time, countries have obvious differences in terms of their economy, science, technology, and other aspects [9]. How to identify the differentiated international environment and the influencing factors of bilateral or multilateral technical cooperation is an urgent problem that needs to be solved.

In terms of the data sources used to explore key areas of the technical cooperation network, some scholars study the published findings of authors from the cooperating countries [7,10]. At present, research on the technical cooperation network among B&R countries is mainly carried out by Chinese scholars. From the perspective of the overall network, the implementation of the network for technical cooperation among B&R countries should be broken down into different time periods, to track the evolution of the network structure and the location of national core nodes. At the same time, it is also necessary to analyze the specific technical fields [11], and in this respect, the cooperation network presents an unbalanced development mode. In addition, some scholars present the network dynamics of the B&R countries from the macro, medium, and micro perspectives [12]. In terms of the definition of cooperation, some scholars define it by reference to the nationality of patent applicants [13], and others by the nationality of the inventors [9,14]. From the perspective of the research objectives of key countries, China is the country advocating for the Belt and Road Initiative. As such, some scholars have conducted a separate analysis of the patent cooperation situation between China and other B&R countries [11], and have explored the evolutionary process of the technical cooperation field by analyzing key information relating to these patents [6].

According to the theory of technology diffusion and knowledge sharing, the high knowledge stock [15] of patent cooperating countries, as well as their high innovation activity [16], have a positive effect on attracting international technological cooperation. In recent years, with the development of multidimensional proximity theory, research on the influencing factors of cooperation between countries has been extended to geographic proximity, cultural proximity, technological proximity, social proximity [15,17], and so on. Research methods are diverse: for example, negative binomial regression is used to explore the driving factors of patent cooperation [18], and QAP is used to analyze the influence relationship between multidimensional proximity [19]. Some scholars also reverse-analyzed the influence of participating in international technical cooperation on the cooperating countries and proposed the influence mechanism of international technical cooperation on social development, the capacity of R&D ability [5], the promotion of the exchange of scientific research personnel between countries, and the patent quality of cooperating countries [9]. In summation, most of the existing studies focus on the structural changes of the Belt and Road technical cooperation network, and there are few studies on the factors influencing the formation of cooperation relations between countries. Meanwhile, traditional statistical methods are generally adopted in the research methods, which impose certain limitations on the research objects and data requirements.

Patents are an effective form of technology protection that affords patent holders certain rights. Therefore, in this paper, we use patent data of cooperating countries in the Belt and Road Initiative as the object of our research [20,21] and we analyze the influencing factors on international patent cooperation by reference to those countries. Considering the complexity of the patent cooperation network, we use an exponential random graph model of social network analysis. The structure of this paper is as follows: Section 2 presents and discusses the research hypothesis. Section 3 includes details of the study design, variable data, and research methods. Section 4 contains empirical and research results. Section 5 presents our conclusions.

2. Research Hypothesis

According to social network theory, cooperative networks consist of points of participating actors and lines representing social relations. Borgatti et al. [22] pointed out four types of relations: similarity, social relations, interactions, and flows [23,24]. Similarity occurs when two nodes have certain attributes in common, such as a similar identity, effects, etc.; social relationships are based on cognitive relationships between nodes, such as cooperation or noncooperation, like or dislike; interactions refer to the behavioral relationship between nodes, which measures the degree of cooperation between nodes; and flows are based on the transitivity between nodes, and the transitivity passing through the nodes in the network forms the unique structural characteristics of the network [22,25]. Based on the above theoretical basis, the international patent cooperation network analyzed in this paper can be divided into three influencing factors [26,27]: node attribute (node similarity), covariates among nodes (common social relations of nodes), and structural relations of the nodes in the network (transitivity among nodes and structural terms represented by structure).

2.1. Node Attributes

Technological innovation strength is closely related to basic scientific research, and a country’s basic scientific strength helps to promote technological progress. Basic research promotes the development of applied technology through the process of original knowledge accumulation and innovative education [28]. These factors form a two-way spillover effect in both spiral promotion and the promotion of interactive growth. Therefore, we formed the following hypothesis:

Hypothesis 1a (H1a).

There is a positive effect between a country’s basic scientific research ability and its participation in international technical cooperation.

Financial ability is the basic, underlying support factor in scientific and technological development, while scientific and technological development can affect economic development. By evaluating the effects of scientific and technological factors according to different economic development conditions, we can identify the endogenous economic growth power of technological progress [29], which also affects a country’s participation in international technical cooperation. Therefore, the following hypothesis is proposed:

Hypothesis 1b (H1b).

There is a positive effect between a country’s financial ability and its participation in international technical cooperation.

Some studies have shown that the stronger the research and development ability of a partner, the more willing it is to carry out foreign cooperation. A country with strong technological strength can have a positive technological spillover effect on cooperating countries [15], which is conducive to attracting technological demand from technologically weak countries. At the same time, technological strength is also conducive to attracting cooperation from technological powers, and cooperation among strong countries can help countries jointly tackle key technological projects to achieve win-win results. Therefore, we formed the following hypothesis:

Hypothesis 1c (H1c).

There is a positive effect between a country’s technological innovation ability and its participation in international technological cooperation.

2.2. Concomitant Variable

With the globalization of the technology market, increasingly technologies are developed at home and are then expanded into overseas markets. As an effective form of technology protection, patents have strong regional characteristics, so the distribution of transnational patent applications is inevitable. The distribution of patents between countries is conducive to the integration of domestic technology and the technology of applicant countries [15]. The process of international technological spillover also promotes the formation of technical cooperative relationships [30], which reflect the active degree of social cooperation between countries. Therefore, we formed the following hypotheses.

Hypothesis 2a (H2a).

The technological spillover proximity between two countries promotes the formation of bilateral technical cooperation.

Many studies have proven that geographical proximity has positive effects on all kinds of technical cooperation. Geographical proximity creates convenient conditions for cooperating parties and saves communication costs due to the short distance between them [13]. This is conducive to a technological spillover effect in the main body of the cooperation and promotes technological integration [31]. Therefore, the following hypothesis was proposed:

Hypothesis 2b (H2b).

Having geographical proximity between two countries promotes the formation of bilateral technical cooperation.

When the industrial-technological development direction among countries is similar there is a natural tendency towards technical cooperation. Technological proximity is conducive to industrial generic technology R&D [17]. Some studies have shown that technological proximity plays a significant positive role in coordinating patentee’s trans-regional knowledge cooperation and in spillover effects [32]. Therefore, we formed the following hypothesis:

Hypothesis 2c (H2c).

Technological proximity between two countries promotes the formation of bilateral technological cooperation.

2.3. Structural Items

Information transfer among organizations with common partners in the network is more effective, and a cooperative relationship is more likely to be established between such parties. It is beneficial to understand the factors involved in the formation of the cooperation network in order to study its expansion and the intermediary cooperation structure among B&R countries. In assessing the impact of the B&R joint initiative, we verify whether network development has gradually spread from the network structure to the core countries and then to the non-core countries. At the same time, we verify whether there are multiple cooperating countries between two cooperating countries, so as to observe the cooperation transitivity of B&R countries. Therefore, geometrically weighted edge sharing partners (GWESP) and geometrically weighted two-tuple sharing partners (GWDSP) [33,34] were selected as the measurement methods of complex structures in the network.

GWESP is known as a “closed triangle relationship” that focuses on network connectivity. GWESP is a triangle relationship in the network, that is, there are three nodes sharing three edges. A node can form a triangle relationship with multiple other nodes, which reflects the tightness of connectivity in a network. As shown in Figure 1, m–n–i, i–n–m, and m–i–n share mutual edges, and so on, for nodes o and p. GWDSP is known as an “open triangle relationship”, which focuses on the number of binary relationships that have shared partnerships [35]. As shown in Figure 1, m–n–i, m–n–o and m–n–p are mutual sharing partners, which explains how a node indirectly transmits a cooperative tendency to another node through multiple intermediate nodes. On the one hand, adding a structure item can prevent approximate degradation in the process of network modeling [36], and on the other hand, it can explain the formation process of a network structure and improve the analysis ability of the model. Therefore, we formed the following hypothesis:

Hypothesis 3a (H3a).

The formation of cooperative relations in the network is affected by transitivity and connectivity.

3. Research Design

3.1. Variable Data

The Belt and Road Initiative advocates openness and a win-win relationship; there is no specific geographical or time limit. Although the Belt and Road Initiative was officially proposed in 2013, it has a foundation of cooperation dating back to prior to 2013. Therefore, this paper relates to data from 2009 to 2018.

The explained variable: A total of 65 countries (United Arab Emirates, Afghanistan, Albania, Armenia, Azerbaijan, Bosnia and Herzegovina, Bengal, Bulgaria, Bahrain, Brunei, Bhutan, Belarus, China, Cyprus, Czech Republic, Estonia, Egypt, Georgia, Greece, Croatia, Hungary, Indonesia, Israel, India, Iraq, Iran, Jordan, Kyrgyzstan, Cambodia, Kuwait, Kazakhstan, Laos, Lebanon, Sri Lanka, Lithuania, Latvia, Moldova, Montenegro, Macedonia, Myanmar, Maldives, Malaysia, Nepal, Oman, Philippine, Pakistan, Poland, Palestine, Qatar, Romania, Serbia, Russia, Saudi Arabia, Singapore, Slovenia, Slovakia, Syria, Thailand, Tajikistan, Turkmenistan, Turkey, Ukraine, Uzbekistan, Vietnam, and Yemen) in the Belt and Road Initiative were selected as research objects, and the data of jointly applied patents among these countries were used to represent technical cooperation. The data came from the WIPO database and was obtained by searching for “nationality of applicant: country A and nationality of applicant: country B” in pairs, forming an adjacency matrix of 65*65. Country A or B is one of the 65 countries; nationalities external to this B&R network are not considered in this paper.

The explaining variable: The number of scientific papers published can effectively reflect a country’s scientific research strength, so a country’s basic scientific research capacity is measured by the number of scientific journal papers published. Papers in scientific journals refer to scientific and engineering articles published in the following fields: physics, biology, chemistry, mathematics, clinical medicine, biomedical research, engineering, and technology, in addition to earth and space sciences (sourced from the National Science Foundation, Science and Engineering Indicators). A country’s financial ability is measured by its GDP per capita, according to the World Bank. The technological strength of a country refers to the measure of innovation output as expressed by the number of national patent applications. Due to the large variances in the number of papers published, GDP, and patent applications between countries, at present, exponential random graph models (ERGMs) cannot estimate effective parameters for multi-valued data with excessive differences, and the solution is at the stage of theoretical exploration. Therefore, the data of papers published, GDP, and patent applications were standardized. The method of data standardization was Z-score.

An enterprise entity in one country will sometimes apply for a patent in another country. On the one hand, the entity is protecting its intellectual property rights in another country, and on the other hand, a process of technological knowledge spillover is created [2]. Technological spillovers are conducive to promoting mutual understanding of the knowledge stock of both parties and it also promotes and results in cooperative innovation [37]. Therefore, technological spillover proximity can be measured by the number of mutual patents applied for between the two countries. This shows the activity of social contact between the two countries, and the technological spillover in the early stages provides the basis for technical cooperation at a later stage [24,38]. The relevant data were obtained from WIPO data center.

Since the scope of the B&R countries spans the Eurasian continents, the geographical distance between countries varies greatly. To gain valid values for the simulation model, we processed multi-valued data. If the geographical spherical distance between two countries is less than the median distance among B&R countries, it is defined as proximity and the value is 1; otherwise, it is 0. Data were obtained from the CEPII database. Technical proximity was calculated using the methodology developed by Jaffe [39], $\mathrm{technical} \mathrm{proximity}=\frac{{{\displaystyle \sum }}_{k=1}^n{a}_{qk}{a}_{jk}}{\sqrt{{{\displaystyle \sum }}_{k=1}^n{a}_{qk}^2{{\displaystyle \sum }}_{k=1}^n{a}_{jk}^2}}$. $a_{qk}$ and $a_{jk}$ represent a nation’s q’s and j’s, respectively, with applications for patents in the field of k in terms of total proportion. Except for measurable variables, the network structure will produce a cooperative transfer effect with the expansion of the network scope. GWESP and GWDSP were selected to measure the network structure. The assumptions and corresponding variable values are shown in

Table 1. Hypotheses, network terms, and meanings.

Variable	Statistics Term	Meanings	Topology	Hypotheses
Explained variable	Co-patent	Number of cooperative patent applications
Explaining variable	edges	Number of network edges	○⸺○
	Research ability (nodecov. RA)	Number of academic paper published	○⸺●	H1a
	Financial ability (nodecov. FA)	Per capita gross domestic product	○⸺●	H1b
	Technological innovation ability (nodecov. TIA)	Number of patent applications	○⸺●	H1c
	Technological spillover proximity (edgecov. SP)	Total number of patents filed between two countries		H2a
	Geographical proximity (edgecov. GP)	Spherical geographic distance		H2b
	Technical proximity (edgecov. TP)	Proportion of patent applications by technology field		H2c
	GWEDSP	Geometric weighted edge sharing partner		H3a
	GWDSP	Geometric weighted two-tuple sharing partner

. The first and second columns are the variable names, the third column explains the variable, and the fourth column is the topological structure of the variable. A topology diagram of “○⸺●” indicates whether countries with strong node attributes are more inclined to cooperate, while “ ” indicates whether countries with relationships in other networks are more likely to cooperate.

In this paper, patent data are used to measure different concepts and, although different indicators are computed, depending on the final goal, there may be variable correlations. However, a fundamental concept underpinning ERGMs is the dependency between network relationships, and without some form of dependency between relationships, a tendency to form certain relationship patterns cannot exist. ERGMs can integrate dependencies and they are a suitable method for understanding network relationship patterns [26].

3.2. Research Methods

Earlier research has shown that node attributes, other cooperation relationships, and node similarity in the network play important roles in the establishment of node relationships [27]. However, traditional statistical methods depend on the irrelevance of variables, an important prerequisite for the assumption of independence. In fact, the relationships of variables are complex and diverse, in being affected by both the surrounding environment and internal factors. Traditional measurement methods also cannot consider the matrix relationship in a network. However, ERGMs [40] can deal with a variety of structural features and node attribute factors in a network. They can also combine the relationships between nodes, which is more comprehensive than traditional statistical methods, and no assumption of independence between variables is required.

ERGMs are probabilistic models for understanding network structures in social network analysis, which were originally proposed by Frank and Wasserman [34,41]. ERGMs cover node attributes, interaction terms, classification terms, structural terms, network covariables, and other variable forms [42], which can systematically show the internal influencing factors of network formation [26]. However, traditional ERGMs only apply to static cross-sectional data. Temporal exponential random graph models (TERGMs) are an extension of ERGMs [43]. Although based on ERGMs, in TERGMs, time series factors are added and considered. TERGMs can also consider node attributes, structural items, and covariates, which are applicable to the panel data in this paper. The data are from 2009 to 2018 and are divided into four time periods. Therefore, two model methods are used in this paper: one is TERGMs, with 5 years selected as the time span, and the other is static ERGMs, with four time nodes of 2009, 2012, 2015, and 2018, used to analyze the static cooperation factors. The calculation methods all use Markov chain Monte Carlo estimation (MCMC) [44,45]. Therefore, the TERGMs and ERGMs used meet the research needs of assessing the influencing factors of the network formation. In addition to providing a new perspective for the study of international technical cooperation networks, the TERGMs and ERGMs used also supplement the deficiencies of existing research on cooperation among B&R countries. In this study, the data were analyzed with an R-statnet suite in the R language [46], using ergm, network, sna, btergm, and other software packages.

3.3. Model Foundation

ERGMs are established based on node attributes, covariates, and structural items [47,48]. Based on ERGMs, TERGMs add time factors.

ERGMs are modeled as follows (Equation (1)):

$$\begin{array}{c}\mathrm{P}\left(\mathrm{X}=\mathrm{x}|\mathsf{\theta }\right) = \left(1/e\right)\exp ({\theta }_{edges}{\rho }_{edges}++{\theta }_{RA }{\rho }_{RA}+{\theta }_{FA}{\rho }_{FA}+{\theta }_{TIA}{\rho }_{TIA}+{\theta }_{SP}{\rho }_{SP}\\ +{\theta }_{GP}{\rho }_{GP}+{\theta }_{TP}{\rho }_{TP}+{\theta }_{gwesp}{\rho }_{gwesp}+{\theta }_{gwdsp}{\rho }_{gwdsp})\end{array}$$

(1)

TERGMs are modeled as follows (Equation (2)):

$$\begin{array}{l}Pn\left(X^t=x^t|X^{t-n},\dots ,X^{t-1},\theta \right) =\\ \exp [{\theta }_{edges}{\rho }_{edges}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)+{\theta }_{RA} {\rho }_{RA}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)+\\ {\theta }_{FA}{\rho }_{FA}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)+{\theta }_{TIA}{\rho }_{TIA}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)+{\theta }_{SP}{\rho }_{SP}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)+\\ {\theta }_{GP}{\rho }_{GP}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)+{\theta }_{TP}{\rho }_{TP}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)+\\ {\theta }_{gwesp}{\rho }_{gwesp}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)+{\theta }_{gwdsp}{\rho }_{gwdsp}\left(x^t,x^{t-1},\dots ,x^{t-n}\right)]/\mathrm{e}\left(\theta ,x^{t-n},\dots ,x^{t-1}\right)\end{array}$$

(2)

$X$ represents the network form, $t$ represents a certain time point, $n$ is the period before the time point, $t$, edges is the number of network edges, $\rho$ represents the variable statistics item, $\theta$ represents the correlation coefficient, and $\mathrm{e}\left(\theta \right)$ is the standardized constant.

4. The Characteristic Fact Analysis

The line chart formed by the number of patent cooperation in each year studied is shown in Figure 2. The total number of patent cooperation in the Belt and Road region showed an upward trend and then a downward trend during the study period. It increased slowly from 2009 to 2011, reached a peak in 2011, and then declined rapidly. After the Belt and Road Initiative was proposed in 2013 the number of engineering projects between countries increased, such as railway bridge construction, urban infrastructure construction, etc., and some technical cooperation was completed during the project implementation process, resulting in a decrease in the number of technical cooperation in the form of patent applications. Since then, the number of annual cooperation has stabilized, remaining at about 500.

The network indicators can reveal the network structure and characteristics from all aspects. Therefore, in this study, we used UCINET software to analyze the patent cooperation network for B&R countries. The number of nodes, node connections, density, diameter, average path length, average clustering coefficient, and average degree was measured annually on the network [49,50]. The results are shown in

Table 2. Network indicators.

Indicators	2009	2010	2011	2012	2013
Nodes	63	63	64	64	64
Node connections	620	654	690	722	736
Density	0.317	0.335	0.342	0.358	0.365
Diameter	3	3	3	3	3
Average path length	1.720	1.693	1.678	1.654	1.641
Average clustering coefficient	0.747	0.767	0.771	0.777	0.779
Average degree	19.683	20.762	21.562	22.562	23
	2014	2015	2016	2017	2018
Nodes	64	64	64	64	64
Node connections	741	746	754	756	763
Density	0.368	0.37	0.374	0.375	0.378
Diameter	3	3	3	3	3
Average path length	1.640	1.636	1.631	1.627	1.627
Average clustering coefficient	0.782	0.781	0.778	0.77	0.771
Average degree	23.156	23.312	23.562	23.625	23.844

.

Since 2009 the number of nodes has stabilized at 63 or 64, indicating that most B&R countries have participated in network cooperation. The number of node connections increased significantly, from 620 in 2009 to 763 in 2018. Although the overall number of cooperative patents declined (as shown in Figure 2), cooperation became more intensive. The average degree indicators in Table 2, show that cooperation between countries gradually increased from 19.683 to 23.844. The rapid growth period was from 2009 to 2013, which indicates that a cooperation network among B&R countries had been formed at this stage, and this cooperation foundation is obvious from the data.

Since 2009, the value of the network density remained above 0.3, and it continued to rise, illustrating that the B&R patent cooperation network is not a sparse network. Cooperation relationships are gradually strengthened, which helps to promote the dissemination of knowledge, and B&R countries tend to establish cooperation relationships. The network diameter remained stable at 3, while the average path length gradually decreased, indicating that efficiency and connectivity improved. The average clustering coefficient was above 0.7, revealing that participating countries are closely connected and network cohesion is strong. The network is a small-world network, which is reflected in indicators such as a shorter average path length and a larger clustering coefficient. From 2009, the average path length showed a downward trend, and the clustering coefficient showed a staggering upward trend, from 0.747 in 2009 to 0.771 in 2018. The main reason for this was the reduced cost of transportation and communication and the existence of faster cooperation channels which promoted an increase in the frequency of cooperation. Countries with high connection points act as public connections in the process of network formation.

5. Result and Discussion

5.1. Descriptive Statistics

Descriptive statistics were performed on the data according to four time nodes: 2009, 2012, 2015, and 2018.

Table 3. Descriptive Statistics of Variables.

2009	Maximum	Minimum	Median	Mean	Standard Deviation
Co-patent	4958	1	4	32.81	215.48
nodecov. RA	286,371.9	2.95	762.95	8795.84	35,850.07
nodecov. FA	59,094.44	0	4950.30	9753.49	11,630.77
nodecov. TIA	241,262	0	213	5119.91	29,787.52
edgecov. SP	557	1	3	18.40	63.21
edgecov. TP	0.94	0.01	0.41	0.41	0.22
2012	Maximum	Minimum	Median	Mean	Standard Deviation
Co-patent	7234	1	4	42.11	291.88
nodecov. RA	329,015.4	8.94	1013.01	10,707.14	41,605.63
nodecov. FA	85076.14	0	6675.19	12,158.83	15,388.09
nodecov. TIA	561,022	0	156	10,291.49	69,005.92
edgecov. SP	1366	1	3	27.47	129.40
edgecov. TP	0.92	0.03	0.46	0.47	0.21
2015	Maximum	Minimum	Median	Mean	Standard Deviation
Co-patent	7611	1	5	44.66	306.57
nodecov. RA	407,974.61	6.2	1288.51	13,082.78	51,695.51
nodecov. FA	63,039.06	0	5840.05	10,589.51	12,341.44
nodecov. TIA	1,009,670	0	235	17,292.34	124,153.20
edgecov. SP	1681	1	3.5	29.26	135.59
edgecov. TP	0.97	0.01	0.45	0.45	0.24
2018	Maximum	Minimum	Median	Mean	Standard Deviation
Co-patent	7955	1	5	45.60	317.62
nodecov. RA	528,263.3	3.69	1776.31	17,024.15	67,146.23
nodecov. FA	66,188.78	0	6966.64	12,230.22	13,936.36
nodecov. TIA	1,459,258	0	216	24,521.63	179,425.91
edgecov. SP	2859	1	3	36.98	211.27
edgecov. TP	0.95	0.02	0.49	0.49	0.21

lists the descriptive statistical results of the variable data. The whole sample included 65 countries, and the descriptive data were measured by maximum, minimum, median, mean, and standard deviation. As shown in Table 3, the data of cooperative patents (co-patents)—the extent to which different counties participate in the cooperation process, varies. The maximum value in 2009 was 4958, whereas it was 7955 in 2018. During the same period, the standard deviation increased from 215.48 to 317.62. In 2009, the median of co-patents was 4 and the mean was 32.81. In the following years, the mean increased, reaching 45.60 in 2018, indicating a large difference among B&R countries in foreign cooperation and that the core countries have a high frequency of cooperation. Additionally, there are some isolated countries that are rarely connected in cooperative networks. Other variables, such as nodecov. RA, nodecov. FA and nodecov. TIA were highly differentiated, showing that the scientific research strengths and basic conditions between countries are also quite different. Over time, the difference in indicators became more pronounced, reflecting that the basic situation conditions of the B&R countries is uneven.

5.2. Results

Table 4. Results of TERGMs.

Variable	Statistics Term	Model1	Model2	Model3	Model4
Baseline effect	edges	−0.86 (***)	−0.65(***)	−2.11(***)	−1.98(***)
Main effects	nodecov. RA		2.77(***)	1.93(***)	2.26(***)
	nodecov. FA		0.06(***)	−0.15(***)	−0.14(***)
	nodecov. TIA		−2.29(***)	−1.54(***)	−1.75(***)
	edgecov. SP			0.32(***)	0.30(***)
	edgecov. GP			0.39(***)	0.40(***)
	edgecov. TP			3.26(***)	2.48(***)
Structural effects	gwesp				0.21
	gwdsp				-0.14(***)

‘***’ p < 0.001.

and

Table 5. Results of ERGMs.

Variable	Statistics Term	2009	2012	2015	2018
		Model5	Model6	Model7	Model8
Baseline effect	edges	−15.36(***)	−0.51(***)	−0.71(***).	−0.53(***)
Main effects	nodecov. RA	0.96(***)	4.31(***)	4.06(***)	3.94(***)
	nodecov. FA	−0.08(*)	−0.21(***)	−0.13(**)	−0.04
	nodecov. TIA	−0.41(*)	−3.74(***)	−3.50(***)	−3.38(***)
	edgecov. SP	2.46(***)	1.54(***)	1.30(***)	1.50(***)
	edgecov. GP	13.04(***)	0.44(***)	0.48(***)	0.76(***)
	edgecov. TP	1.19(***)	0.73(***)	1.00(***)	0.70(***)
Structural effects	gwesp	0.36	−0.47	−0.40	−0.49
	gwdsp	−0.12(***)	−0.20(***)	−0.18(***)	−0.20(***)

‘***’ p < 0.001, ‘**’ p < 0.01, and ‘*’ p < 0.05.

set out the TERGMs and ERGMs analysis results, respectively, and the results are basically the same.

(1)

The research ability (nodecov) in node attributes was both positive and significant in annual results, indicating that basic scientific research strength helps B&R countries to strengthen cooperation with outside countries, as these countries tended to develop international technical cooperation. Hypothesis H1a is therefore verified. Financial ability (nodecov) was negative and significant—the estimated result of financial actors in TERGMs was −0.14 (***), and in ERGMs the results were −0.08(*), −0.21(***), −0.13(**), and −0.04. Although the data in 2018 were not significant, they did not affect the result. The economic levels of B&R countries are quite different. Although an economic foundation is a necessary guarantee for technological research and development, B&R countries do not establish cooperative relationships due to economic factors, with economic factors having the opposite effect. Thus, hypothesis H1b was not established. Technological innovation ability (nodecov) does not promote cooperation but has a counterproductive effect. The result in TERGMs was −1.75(***), and in ERGMs the results were significantly negative. Countries with strong R&D strength do not tend to cooperate with foreign countries, which may be related to their concerns about key technology leakage. Hypothesis H1c is untenable.

(2)

Technological spillover proximity (edgecov), geographical proximity (edgecov), and technical proximity (edgecov) were significantly positively in TERGMS and ERGMs; therefore, H2a, H2b, and H2c were verified. Geographical proximity was shown to have a positive impact on the formation of cooperative relations. China is adjacent to South Korea, India, and Russian territories, and the number of cooperation in patent applications was significantly higher than with other countries. The mutual patent application between countries in technological spillover proximity is conducive to an in-depth understanding of each other’s national conditions, which improves the chances of later cooperation. At the same time, a level of technological similarity is a prerequisite and necessary condition for technological cooperation.

(3)

GWESP is not significant, indicating that when other factors remain unchanged, compared with a random network, the connectivity of the network has no significant impact. GWDSP is negative and significant, showing that it is not easy to form a shared open triangle structure in the cooperation network along the Belt and Road. The closeness of cooperation between countries is not enough; the cooperation network presents a situation where the whole is scattered and the parts are gathered, and a mediating effect is not obvious. This fact can be interpreted as the probability of establishing cooperation among the B&R countries being smaller than the probability of cooperation between two nodes in a random network. Thus, the assumptions of H3a are not supported.

5.3. Stability test

In this paper, both TERGMs and ERGMs were used to simulate empirical results from both panel data and cross–sectional data, and the results of the dual methods are consistent. While TERGMs and ERGMs both use Monte Carlo maximum likelihood estimation, the stability test adjusts the estimation algorithm. TERGMs use the bootstrap method (btergm) [51] to estimate and ERGMs use a maximum pseudo likelihood estimation (MPLE). Due to space limitations, the results of the TERGMs and the results of the ERGMs in 2009 and 2018 are shown in

Table 6. Results of the stability test.

Variable	Statistics Term	Adjusted Estimation Algorithm
		TERGM	ERGM2009	ERGM2018
Baseline effect	edges	−2.18 # [−2.33; −2.06]	−2.62(***)	−1.54(**)
Main effects	nodecov. RA	0.90 # [0.77; 0.98]	0.91(***)	4.55(***)
	nodecov. FA	−0.05 # [−0.07; −0.03]	−0.07	−0.01
	nodecov. TIA	−0.36 # [−0.43; −0.30]	−0.42(*)	−3.82(***)
	edgecov. SP	0.37 # [0.25; 0.77]	2.44(***)	1.35(***)
	edgecov. GP	0.40 # [0.33; 0.45]	0.38(***)	0.81(***)
	edgecov. TP	2.67 # [2.43; 2.96]	1.68(***)	0.82(***)
Structural effects	gwesp	0.30 # [0.26; 0.34]	0.17	0.22
	gwdsp	−0.09 # [−0.11; −0.08]	−0.08(***)	−0.30(***)

The value in square brackets is 95% confidence interval, # means 0 is not in the confidence interval. ‘***’ p < 0.001, ‘**’ p < 0.01, and ‘*’ p < 0.05.

. The results are basically consistent with the above, and the results are stable.

5.4. Discussion

In this paper, TERGMs and ERGMs are used to study the influencing factors of the patent cooperation network among B&R countries. Analysis of the results shows the following:

• First, the basic scientific research ability, technological spillover proximity, geographical proximity, and technological proximity of B&R countries all promote participation in patent cooperation. The economic strength of a country has no significant impact on a country’s participation in patent cooperation, indicating that economic strength is not an influential factor in cooperation among B&R countries. This does not mean that there will be more cooperation between countries with a high level of economic development. The B&R countries straddling the Eurasian continents have different levels of economic development, which weakens the influence of financial ability.
• Secondly, it can be seen from the specific data that the technological innovation ability variables of the B&R countries straddling the Eurasian continents have different levels, which weakens the influence of technological ability. Technical strength variables have a negative impact on cooperation. On the one hand, the negative impact on cooperation may be due to the fact that most B&R countries are developing countries. As such, they tend to have domestic R&D or domestic cooperation, and there is not a lot of international cooperation, which will reduce the stock of international patent cooperation to some extent. On the other hand, the negative impact on cooperation may be affected by the extensive foreign cooperation between major countries, for example, China, India, Singapore, and other countries, whose focus may not necessarily be on the developing B&R countries. Technological spillover proximity has a significant positive effect on patent cooperation, and the distribution of the mutual patent application among countries promotes technological integration. Geographical proximity is significant at each time node, indicating that the closer countries are in terms of distance, the more beneficial it is to establishing cooperative relations between them. Technological proximity has been positive, and B&R countries have cooperation advantages in strategic emerging industries. Technological proximity can play to the strengths of both partners in joint efforts.
• Thirdly, by studying the network structure, the model parameter estimation results of GWDSP are significantly negative. This shows that the structure of the network itself does not affect the formation of network node relations, that the network does not tend to use intermediary multi−path cooperation, and that the cooperation network of B&R countries has particularities compared with a random network.

6. Conclusions

In the field of cooperative network research, the driving factors of network cooperation multiply as a network evolves in time and space, and the influencing factors become increasingly diverse. Most existing research has focused on descriptive research of the network structure, but an analysis of the intrinsic structural causes is limited. This paper looks deeply into the formation of the B&R countries’ cooperation network and comprehensively considers a wide range of aspects, such as economic systems, activities, and technological development, from the perspective of the national environment. In terms of research methods, TERGMs and ERGMs can analyze various factors of national characteristics, activities between countries, and the network structure and carry out a comprehensive evaluation of network causes. At the same time, B&R countries are spread throughout the Eurasian continents, and the cooperating countries have different national conditions. Therefore, we adapted the research method to deal with the specific characteristics of the network, producing an innovative research method to assess international technical cooperation.

The conclusions of our analysis show that economic factors and technological innovation have no positive impact on the promotion of cooperation. An economic foundation is the material guarantee for scientific research, and many scholars have studied the mutual promotion effect of an economic foundation on technological innovation in international cooperation [52], but the research object of this paper is the countries along the Belt and Road. There is a large disparity in the economic levels between countries along the Belt and Road, most of which are developing or underdeveloped regions. In this part of the world, economic factors have a less positive impact on technical cooperation than other factors, which differs from the general international technical cooperation conclusion. Considering the impact of technological innovation, strong technological innovation can certainly improve the efficiency of innovation, but the B&R countries are quite different, and some countries in the network are far ahead of the peripheral countries in the number of patent applications. Some studies have shown that countries with robust technological innovation strength do not need to rely on external cooperation to a certain extent, and they may reduce cooperation contacts due to concerns about the leakage of key technologies [53]. This conclusion is verified in this paper. The number of international cooperation patents in B&R countries is relatively small compared to the number of local patent applications, which also points to the counteractive impact of technical innovation factors. Therefore, entities with strong technological innovation capabilities are likely to form a lock–in effect on cooperation [35] and put forward higher requirements for technical cooperation along the Belt and Road.

Furthermore, in addition to using TERGMs and ERGMs to study node attributes and the network structure, this paper also explores the role of cooperative proximity in the formation of spatial relationships and considers technological proximity, geographic proximity, and technological spillover proximity. Our research shows that these factors all affect the formation and development of networks, which supports the theory and practice of multidimensional proximity. As the country advocating the Belt and Road Initiative, China strengthens the cooperation among B&R countries by promoting technological exchanges between countries, enhancing the market reciprocity of patent distribution, increasing international cooperation in scientific and technological projects, and via other measures. It is worth noting that China’s economic factor is not obvious; what is more conducive to the gradient flow of technical cooperation between economically developed and developing countries, is that China, as a developing country in the Belt and Road Initiative, can connect technology leaders and cooperate with laggard countries, thus connecting technology R&D and encouraging market expansion. Based on the proximity of technologies, it is suggested that cooperation should be developed in basic scientific research, and cooperation in advanced applied technologies should be promoted. Attention should be paid to the impact of technological spillover proximity to enhance the recognition of joint initiatives, technology knowledge exchanges, mutual trust in political systems, and to promote bilateral and multilateral technical cooperation.