Research on the Enterprise Collaborative Innovation Performance in the Economic Circle of Chengdu-Chongqing from the Perspective of Proximity

. Based on the perspective of proximity, in the context of the Economic Circle of Chengdu-Chongqing of China, we use invention patent data provided by the China National Intellectual Property Administration and conduct negative binomial models to empirically test the impact of multidimensional proximity on enterprise collaborative innovation performance. We further examine the moderating effect of enterprise innovation capacity on the relationship between multidimensional proximity and enterprise collaborative innovation performance. The results show that technological proximity, geographical proximity, and institutional proximity all positively affect enterprise collaborative innovation performance. Enterprise innovation capability has a negative moderating effect on the relationship between institutional proximity and enterprise collaborative innovation performance, but it cannot negatively moderate the positive effects of technological proximity and geographical proximity on enterprise collaborative innovation performance


Introduction
In recent years, the development of the Chengdu-Chongqing region of China has caught increasing attention of the government of China, enterprises, and academics. In 2020, the Chinese government issued a master plan for the construction of the Economic Circle of Chengdu-Chongqing in southwest China. The enhancement of enterprise collaborative innovation capability is conducive to the innovation vitality and sustainable development of the Economic Circle of Chengdu-Chongqing.
In the 1990s, the academics began to study innovative activities from the perspective of geographical proximity [1]. With the continuous development of proximity theory, the research in this field has gradually expanded from a single dimension (i.e., geographical proximity) to multiple dimensions. The French school of proximity introduced multidimensional proximity and argued that in addition to geographical proximity, the proximity of other dimensions also affects collaborative innovation. However, there is still great overlap and intersection between the concepts of each dimension of proximity. Boschma (2005) [2] made pioneering research on interactive learning and collaborative innovation from the five dimensions (i.e., cognitive, organizational, social, institutional, and geographical proximity), and set up the basic framework for later research. In recent years, scholars have carried out a lot of research on the antecedents of collaborative innovation performance and obtained fruitful research results [3].
However, there are inconsistent results regarding the effects of multidimensional proximity on collaborative innovation performance. Some results showed that multidimensional proximity positively affects collaborative innovation performance. Some studies found that there is an inverted U-shaped relationship between technological proximity and collaborative innovation performance. Some studies found that each dimension of proximity is alternative or complementary. Therefore, it is necessary to further summarize and integrate the relevant theories, and test the impact of multidimensional proximity on collaborative innovation performance under specific contexts. As a key strategic development place in the western region of China, the Economic Circle of Chengdu-Chongqing provides a suitable context to examine the impact, because this region has many different characteristics, compared with developed areas where scholars have conducted a lot of empirical research.
Based on the perspective of proximity, in the context of the Economic Circle of Chengdu-Chongqing, we explore how technological proximity, geographical proximity, and institutional proximity affect enterprise collaborative innovation performance. We further examine how enterprise innovation capacity moderates these relationships. Utilizing the Chinese invention patent data, we conduct negative binomial models to empirically test our hypotheses. We find that technological proximity, geographical proximity, and institutional proximity have a positive impact on enterprise collaborative innovation performance. We further find that enterprise innovation capacity weakens the positive relationship between institutional proximity and enterprise collaborative innovation performance. Thus, this study enriches the literature on proximity and collaborative innovation.

Technological Proximity and Enterprise Collaborative Innovation Performance
Technological proximity refers to the proximity of two organizations within the technology space [4]. There are many studies on the impact of technological proximity on innovation performance. However, the results are inconsistent. Positive effects, negative effects, and even inverted U-shaped effects have all been empirically supported in existing studies [5]. Some scholars argue that the relationship between technological proximity and collaborative innovation performance is affected by regional innovation capacity. The Economic Circle of Chengdu-Chongqing is located in the west of China. Compared with the developed countries and the southeast coastal areas of China, there is still a gap in the level of technology and innovation in this region. Therefore, the effect of technological proximity on enterprise collaborative innovation performance is mainly positive. In this context, technological proximity provides a similar technology base for enterprises, which helps enterprises reduce communication costs, promote the identification, acquisition, absorption, and integration of each other's knowledge, and use complementary knowledge for innovation, thereby improving the efficiency of cooperative innovation. Based on the above analysis, this paper puts forward the following assumptions: Hypothesis 1. Technological proximity has a positive impact on enterprise collaborative innovation performance.

Geographical Proximity and Enterprise Collaborative Innovation Performance
Geographical proximity captures the proximity of physical distance between enterprises [2]. On the one hand, the importance of geographical proximity to collaborative innovation performance has been supported by a large number of empirical studies [6]. Geographical proximity brings individuals together, which facilitates the exchange of information, especially for tacit knowledge [7]. On the contrary, the greater the geographical distance, the more difficult the transmission of tacit knowledge, which is detrimental to the development of collaborative innovation performance. On the other hand, some scholars hold the opposite view that temporary geographical proximity, such as meetings and short visits, can meet the needs of cooperative communication, so it is unnecessary for continuous geographical proximity in the process of cooperation [8]. Schwartz, Peglow, Fritsch and Guenther (2012) [9] argue that with the development of modern communication technology, geographical distance is no longer the main factor affecting collaborative innovation performance. Overall, most research results support the view that geographical proximity has a positive impact on collaborative innovation performance. Although modern information technology has been rapidly developed, tacit knowledge still can't completely be transformed into encoded knowledge, and face-to-face explanation and communication still can't completely be replaced. Geographical proximity can realize frequent face-to-face communication and learning at low cost and effectively transfer tacit knowledge. Therefore, geographical proximity is conducive to the improvement of enterprise collaborative innovation performance. To sum up, this paper puts forward the following assumptions: Hypothesis 2. Geographical proximity has a positive impact on enterprise collaborative innovation performance.

Institutional Proximity and Enterprise Collaborative Innovation Performance
Institutional proximity presents the extent to which organizations share formal and informal regulatory mechanisms, including the practices, rules, laws, and conventions [10]. Not only the formal institution affects organizational innovation performance, such as laws and regulations, but also the informal institution deeply affects the innovation performance of an organization, such as cultural norms and habits [11,12]. Due to the special historical and cultural background of China, there are significant differences in the institutional environment among different regions. Differences in institutional norms, investment plans, and values are harmful to the incentive of researchers, thus hindering the development of collaborative innovation across regions. Institutional proximity means that organizations can share similar values and rules of conduct, which provides a basic level of trust for both sides and reduces uncertainty and transaction costs. Under a similar norm and procedure, organizations can achieve effective knowledge transfer, so as to promote the development of collaborative innovation [2]. Therefore, the following assumptions are made in this paper: Hypothesis 3. Institutional proximity has a positive impact on enterprise collaborative innovation performance.

Moderating Effect of Enterprise Innovation Capacity
Technological proximity, geographical proximity, and institutional proximity can promote enterprise collaborative innovation performance through different mechanisms, but these positive effects may be moderated by enterprise innovation capacity. Enterprises with strong innovation capacity have accumulated a lot of experience and established a large knowledge base [13]. Therefore, these enterprises have a strong ability to learn and integrate knowledge, which is conducive to their understanding, absorption, and recombination of new technologies and knowledge [14]. Then, to a certain extent, they can overcome the adverse effects of low technological similarity and innovate by absorbing knowledge far away from their own knowledge base. Consequently, enterprise innovation capacity weakens the relationship between technological proximity and enterprise collaborative innovation performance. Meanwhile, enterprises with strong innovation capacity have a strong ability to absorb and utilize tactic knowledge [15]. Even if the geographical distance leads to less face-to-face communication, enterprises with strong innovation capacity can overcome the restriction of geographical distance to a certain extent through their own strong understanding and absorption ability, as well as advanced communication technology. Therefore, for enterprises with strong innovation capacity, the relationship between geographical proximity and enterprise collaborative innovation performance may be weakened. Because of their innovation experience and strong adaptability, enterprises with strong innovation capacity can get rid of the discrepancy of institutions to a certain extent, and actively cooperate with other enterprises under different values and incentive mechanisms [16]. Therefore, for enterprises with strong innovation capacity, the relationship between institutional proximity and enterprise collaborative innovation performance may be weakened. On the contrary, for enterprises with low innovation capacity, the proximity of different dimensions can make up for the lack of ability and promote collaborative innovation performance among enterprises. Based on this, this paper puts forward the following assumptions: Hypothesis 4a. Enterprise innovation capacity weakens the positive effect of technological proximity on enterprise collaborative innovation performance.
Hypothesis 4b. Enterprise innovation capacity weakens the positive effect of geographical proximity on enterprise collaborative innovation performance.
Hypothesis 4c. Enterprise innovation capacity weakens the positive effect of institutional proximity on enterprise collaborative innovation performance.

Data and Sample
We combine the information from three authoritative data sources to build a unique database. First, the information regarding patents comes from the China National Intellectual Property Administration (CNIPA). Second, the data about the longitude and latitude of enterprises comes from Chinese Research Data Services (CNRDS). Third, the index data of regional innovation capacity comes from the Evaluation Report on China's Regional Innovation Capacity.
This article selects the invention patent data from 1985 to 2018 and cleans it with the following steps. Firstly, because this article focuses on collaborative innovation between enterprises, we only reserve patents with only two applicants which are enterprises. Secondly, because we focus on the sample of enterprises in the Chengdu-Chongqing region, we have deleted the patents whose first applicant does not belong to the Economic Circle of Chengdu-Chongqing. Thirdly, due to the availability of data, we delete patents including applicants from Hong Kong, Macao, Taiwan, and foreign countries. After screening the original patent data and matching it among the datasets, a total of 2037 patent applications are obtained. Because the dependent variable has a five-year window and the joint patent application data before 2001 are too little, we select the patent data from 2001 to 2014, aggregate them to the enterprise level, and finally obtain 292 observations.

Variables
(1) Dependent Variable The dependent variable is collaborative innovation performance, which is measured by the number of patents jointly applied by the focal firm and other firms [17]. Given that the improvement of collaborative innovation capacity is a long-term and stable process, therefore, we use a five-year window to calculate this variable.
(2) Independent Variables Technological proximity. We use the method developed by Jaffe (1986) [4] to measure technological proximity. The specific formula is as follows. To be specific, f ik represents the total number of invention patents applied by enterprise i in technology class k in the past three years, f jk indicates the total number of invention patents applied by enterprise j in technology class k in the past three years, and m is the number of all technology classes. Technological proximity of an enterprise is measured by calculating the median of technological proximity for the focal enterprise each year.
Geographical proximity. We measure the geographical distance between two enterprises by the spherical distance [18], and the formula is as follows. Specially, i and j represent the cities where the enterprises are located, lat indicates the latitude of the city, lon indicates the longitude of the city, and 6371 is the average radius length of the earth. We logarithmically process geographical distances to remove dimensions. By calculating the median geographical distance of an enterprise for each year, we measure geographical proximity of an enterprise. Moreover, we invert the variable such that a higher value of this variable indicates that the greater the geographical proximity between the two enterprises. Measurement Collaborative innovation performance The number of patents jointly applied by the focal firm and other firms within 5 years.

Technological proximity
The specific formula is shown in Eq. (1).

Geographical proximity
The specific formula is shown in Eq. (2). Institutional proximity If the two enterprises applying for the focal patent are located in the same province, the value is 1; otherwise, it is 0.

Patent scale
The specific formula is shown in Eq. (3).

Company age
The time between the focal year and the first year in which the enterprise applied for a patent.

Cooperation experience
If there is previous cooperation experience between enterprises, this variable is valued as 1; otherwise, this variable is valued as 0.

Regional innovation capacity
The comprehensive indicators of the innovation capacity of each province from the Evaluation Report on China's Regional Innovation Capacity.
Geo i jt = 6371 arccos sin (lat i sin (lat j ) + cos (lat i )) cos (lat j ) cos lon i − lon j Institutional proximity. Following the previous study, we measure institutional proximity by identifying whether the two applicants belong to the same province [18]. If the two applicants applying for the focal patent are located in the same province, institutional proximity is assigned to 1; otherwise, it is equal to 0. We measure institutional proximity of an enterprise by calculating the median of institutional proximity of an enterprise per year. Patent scale. The innovation capacity of enterprises is generally measured by the patent scale of enterprises [19]. According to the method of Hall, Jaffe and Trajtenberg (2005) [20], we use the following formula to measure this variable. In this formula, patentscalet indicates the patent scale of the focal year, patent t indicates the number of patent applications of the focal year, and patentscalet-1 represents last year's patent scale.
(3) Control Variables We also control the age of an enterprise, which may change the organizational conditions in which innovation activities are carried out. Following the prior study [21], we measure the variable by subtracting the year the enterprise first filed for a patent from the focal year. The previous experience of cooperation reduces the uncertainty in collaborative innovation and increases the success rate of collaborative innovation. Therefore, we control cooperation experience. Before the focal year, if there is previous cooperation experience between enterprises, this variable is valued as 1; otherwise, this variable is valued as 0. Moreover, we include regional innovation capacity as a control factor. In provinces with strong regional innovation capacity, enterprises may carry out more collaborative innovation activities. We use the comprehensive indicators of the innovation capacity of each province from the Evaluation Report on China's Regional Innovation Capacity to measure the variable. Finally, we included province dummies, industry dummies, and year dummies to control for the macroeconomic effects and time effects on collaborative innovation performance. A full list of the variables used in our empirical study along with measurements is provided in table 1.

Analysis
Given that our dependent variable is counts of patents, we conduct negative binomial regression [22]. We used the following equations to test our hypotheses respectively. CIP it represents collaborative innovation performance, Tec it stands for technological proximity, Geoit captures geographical proximity, Ins it measures institutional proximity, Pat it−1 represents patent scale,Con it represents the control variables, and ε captures the error term. Meanwhile,β 0 stands for the intercept term. β 1 in 4 represents the impact of technological proximity on collaborative innovation performance, β 1 in 5 represents the impact of geographical proximity on collaborative innovation performance, and β 1 in 6 represents the impact of institutional proximity on collaborative innovation performance. β 2 captures the influence of patent scale, β 3 captures the moderating effect of patent scale, and β 4 indicates the influence of control variables. Table 2 and table 3 present descriptive statistics and correlation matrix for the variables in our studies respectively, except for province dummies, industry dummies, and year dummies. Except for the large correlation between geographical proximity and institutional proximity (-0.871), the correlation coefficients between the other variables are within the allowable range. In order to avoid possible multicollinearity problems, geographical proximity and institutional proximity are not included in the same model in this study.

Hypotheses Tests
The results of negative binomial regression are shown in table 4. Model 1 is the result of all control variables. In Model 2, we add technological proximity to test the impact of technological proximity on collaborative innovation performance. In Model 3, we add geographical proximity to test the effect of geographical proximity on collaborative innovation performance. In Model 4, institutional proximity is added to test the impact of institutional proximity on collaborative innovation performance. Further, we add the interaction terms between patent scale and independent variables in Model 5, Model 6, and Model 7 respectively, to test the moderating effect of enterprise innovation capacity. In Model 2, the coefficient of technological proximity is positive and significant (β = 0.344, p < 0.1), indicating that the impact of technological proximity on collaborative innovation performance is positive and Hypothesis 1 is supported. In Model 3, the coefficient of geographical proximity is significantly positive (β = 0.477, p < 0.01), which is consistent with Hypothesis 2. In Model 4, the coefficient of institutional proximity is positive and significant (β = 0.328, p < 0.05). Thus, Hypothesis 3 is strongly supported.
Hypothesis 4a and Hypothesis 4b, respectively, predict that the enterprise innovation capacity weakens the positive effects of technological proximity and geographical proximity on collaborative innovation performance. However, as shown in Model 5 and Model 6, the results of their interaction terms are not significant. Therefore, Hypothesis 4a and Hypothesis 4b are not supported. The results imply that even if an enterprise has a strong innovation capacity, the positive effects of technological proximity and geographical proximity on collaborative innovation performance may not be diminished. In contrast, the interaction term of institutional proximity and patent scale in Model 7 is negative and significant (β = −0.0889, p < 0.05). Therefore, Hypothesis 4c is corroborated. In order to illustrate this moderating effect, we plot the interaction effect in figure 2 based on the statistics in Model 7 of Table 4, which shows that enterprise innovation capacity weakens the positive effect of institutional proximity on collaborative innovation performance.

Robustness Tests
We conduct several robustness checks 1 . First, we use alternative measures of the variables to test the robustness of our results. We use a five-year window to calculate technological proximity instead of a three-year window. Meanwhile, we use patent scale without multiplied depreciation rate to measure enterprise innovation capacity (The results are shown in table  5). Secondly, subsamples from 2005 to 2013 are selected from all samples for regression to

Discussion and Conclusion
Based on the perspective of proximity, we use Chinese invention patent data to empirically analyze the impact of multidimensional proximity on the enterprise collaborative innovation performance in the context of the Economic Circle of Chengdu-Chongqing. We find that technological proximity, geographical proximity, and institutional proximity positively affect enterprise collaborative innovation performance. We further examine how these relationships are moderated by enterprise innovation capacity. We find that enterprise innovation capacity weakens the relationship between institutional proximity and enterprise collaborative innovation performance, but can't weaken the positive effects of technological proximity and geographical proximity. The results mean that an enterprise with strong innovation capacity can cooperate successfully with other enterprises with large institutional distances, rather than those with large technological distances or geographical distances.
This paper contributes to the literature regarding proximity. First, the effects of multidimensional proximity on enterprise collaborative innovation performance are not consistent in the existing research, especially technological proximity. This study considers the effect of the environment and tests the impact of multidimensional proximity on enterprise collaborative innovation performance in the Economic Circle of Chengdu-Chongqing of China, which is different from other developed areas. Thus, our study enriches the literature regarding proximity. Second, this study examines the moderating effect of enterprise innovation capacity on the relationship between multidimensional proximity and collaborative innovation enterprise. Therefore, our research enriches the literature on proximity dynamics.
Our results have practical implications for the enterprises and government. For the enterprises in the Economic Circle of Chengdu-Chongqing, they should actively select suitable objects within their familiar technological fields to carry out collaborative innovation, make full use of the advantages of similar knowledge bases, absorb complementary knowledge from each other, and improve collaborative innovation performance. Meanwhile, they can collaborate on innovation with enterprises that are geographically or institutionally close to each other, thereby enhancing their innovation capabilities. For the government in the Economic Circle of Chengdu-Chongqing, they should encourage enterprises to set up cooperative innovation so that promote the exchange and communication between enterprises, and stimulate the innovation vitality of enterprises. Meanwhile, the government should attract relevant enterprises to land and promote industrial agglomeration, which provides prerequisites for enterprises to make use of geographical advantages to improve collaborative innovation performance. Further, the government should build a similar incentive policy system and common norms for the enterprises to promote the collaborative innovation.
There are some limitations in this paper that need to be further expanded in the future. Firstly, this study only focuses on the impact of multidimensional proximity on the collaborative innovation of enterprises in the Economic Circle of Chengdu-Chongqing of China. Future research can study the effects of multidimensional proximity on enterprise collaborative innovation performance under different contexts. Secondly, this study focuses on enterprise collaborative innovation, which does not include industry-university collaborative innovation. Future research can take industry-university collaborative innovation as the research object, and pay attention to the collaborative innovation between enterprises and universities. Third, this paper only explores the moderating effect of enterprise innovation capacity. Future research can examine other contingency factors.