Abstract:     An essential task for many Chinese cluster firms nowadays is planning and conducting nonlocal innovative collaboration so as to access to distinct knowledge pools. A large number of studies doubted the influence of spatial distance on cluster firms′ nonlocal innovation. Evidences from both theoretical and empirical researches announced that advanced intelligence communication technology is an effective substitution of face-to-face interaction and thus "the death of geography" becomes one of the most impactful theories in Economic Geography. Besides that, temporary geographical proximity, which benefits cluster firms in keeping them away from falling into lock-in traps, can offset the disadvantage of spatial distance in knowledge diffusion. Otherwise, there are also a group of studies argued that geographical proximity still importance in determining cluster firms′ nonlocal innovative activities since physical distance still negatively affect the construction of nonlocal ties and formation of knowledge network in which actors dispersed in distinct regions. Therefore, whether geographical proximity matters when cluster firms conducting their nonlocal innovative activities becomes a hot topic. Aiming to shed light on this theoretical issue, six hypotheses have been proposed through theoretical review and systematical analysis of both the role of geographical proximity and social proximity on nonlocal innovation of cluster firms. Unlike the majority of previous studies, social proximity has been treated as a moderate variable rather than a mediate factor in this paper since we believe that social relationships between cluster firms and their remote partners are not determined by geographical proximity under nonlocal innovation context. 
     The effect of geographical proximity on nonlocal innovation has been detected based on a sample covers 114 cluster firms, in which 70% of them belongs to high-technology industry such as bio-medicine and electrical & information and mostly are private-owned companies and 30% comes from traditional industry, in Nanjing, Xi′an and Foshan. All those firms announced that they have nonlocal innovative activities in past three years, 86% of them have constructed important collaborative relationships, ranked as top three closest connections at least, with nonlocal organizations and 82.36% interviewees reported that they have conducted cross-boundary collaborative activities more than one year. Our data are collected through semi-structure interview and questionnaire survey to CEO, director of R&D department or manager who is in charge of innovation related affairs. We measure all the variables adopting methodologies provided by related prior researches from renowned publications, and test the reliability and validity through empirical analysis based on our sample data. 
   All the six hypotheses have been tested using hierarchical multiple regressions which allows us identify and discriminate the effect of distinct types of proximities and realize the moderate role of different indicators of social proximity. We estimate our theoretical construct in two steps. First, we investigate the effect of geographical proximity on innovativeness and innovation performance. Then, we put four indicators of social proximity, i.e., relationships durance, communication frequency, the number of nonlocal partner as well as the number of nonlocal institutions, into the regression model so as to test the moderate effect of social proximity on the relationships between geographical proximity and firms′ nonlocal innovation. Our regression results indicate that geographical proximity indeed has positive influence on cluster firms′ innovativeness and innovative performance even when considering the effect of social proximity, i.e., the closer of cluster firms with their nonlocal partners, the higher innovation performance they may gain and more advanced technology they can develop, and thus provide direct evidence that the geography still matters which in line with our expectation. However, social proximity can only partially moderate geographical proximity′s effect on nonlocal innovation. Specifically, the number of nonlocal institutions can significantly affect the relationship between geographical proximity and innovativeness. In other word, cluster firms′ nonlocal subsidiaries significantly benefit their innovation collaboration with distant partners. Besides that, relationships durance, number of nonlocal partner as well as number of nonlocal institutions all play significant moderating role on the relationship between geographical proximity and innovation performance. Thus, keeping sustainable interaction, connecting diverse nonlocal collaborators as well as setting up more subsidiaries in distant regions can help cluster firms improve their innovation performance. From above results, we can conclude that the influence of spatial factors cannot be eliminated by social proximity. Thus, we provide indirect evidence that geography still matters. Our results also reveal that only two indicators of social proximity, i.e., the number of nonlocal partner and the number of nonlocal institutions, are positively related to cluster firms′ nonlocal innovation. However, relationships durance and communication frequency, highlighted by many researches as important factors to interaction during the co-invent process, have insignificant relationship with nonlocal innovation. Finally, the reason why our findings are inconsistent with prior studies has been discussed and how to dissolve present theoretical divergence under multi-dimensional proximity frame has been analyzed. 
   Theoretical contributions of this paper are twofold. First, this research adds to the current literature by responding to the debate of the role of geography in cluster firms′ nonlocal collaboration. Our empirical results support the positive influence of geographical proximity in cluster firms′ nonlocal innovation which provides new evidence for the view that "geography matters" under nonlocal innovation context and in line with the literature of economic geography. Second, we claim that the present theoretical conflict around the role of geography proximity can be reconciled based on the multiple proximities frame. Specifically, cluster firms may not seek to substitute one kind of proximity with another one during nonlocal innovation. Instead, strategy that making better use of various dimensional proximities may be more attractive to them. In conclusion, our findings support the needs to integrate both geography proximity and social proximity into theoretical frame when considering nonlocal innovation activities. To managers who endeavor to construct nonlocal connections and improve firms′ innovation performance, our findings also have several practically implications. For one side, managers should consider spatial distance as a key factor when building co-invent relationships beyond local cluster and clarify the boundary of firms′ nonlocal territory properly. For another thing, it is useful for managers to take advantage of the mutual effect of geographical proximity and social proximity in acquiring nonlocal innovative resources through setting up nonlocal institutions and cultivating social capitals with nonlocal partners so as to rise opportunities to access to distinct knowledge networks.

Key words: cluster firm, geographical proximity, social proximity, technological proximity, nonlocal innovation