Abstract:    Innovation has become the core driving force of regional economic growth. It is of great significance to study the influence of inter-regional flow of R&D elements and its spatial spillover effect on innovation efficiency. Based on panel data of 30 provinces in China from 2001 to 2016, this paper uses super-efficiency DEA model and improved gravity model to measure the innovation efficiency and R&D elements flow in different regions, and establishes the Spatial Durbin Model to explore the difference of R&D elements flow and its spatial spillover effect on innovation efficiency.
    First of all, through the super efficiency DEA model to evaluate the development level of innovation efficiency in different regions of China. It is found that there is a large gap in innovation efficiency in different regions. The top five regions of average innovation efficiency are mainly located in the eastern region, and the last five regions are all located in the central and western regions. The innovation efficiency gap between regions is obvious. During the investigation, the average value of innovation efficiency in the eastern region has been higher than the national average, although there is a slight decline. It is still the leading region of innovation and development in China; the northeast region has a good momentum of innovation efficiency rise; the innovation efficiency in the central and western regions has been lower than the national average, but the overall development of the central region is stable, and the western region has a fluctuating rise, but the latter has a clear momentum of innovation and development catch-up. 
   Secondly, the improved gravity model is introduced to measure the inter-regional inflow and outflow of R&D elements in each region, and it is taken as the core explanatory variable. Four control variables, namely government support, infrastructure, industrial structure and human capital, are introduced to establish the spatial Doberman model of R&D personnel flow and the spatial Doberman model of R&D capital flow, respectively, so as to further explore the differences. The inflow and outflow of R&D factors among regions and the spatial spillover effect on regional innovation efficiency are different. From the global Moran index test results, it is found that in most years, there is a significant positive spatial autocorrelation of innovation efficiency in China, that is, there is a strong spatial dependence of innovation efficiency in each region, and the innovation efficiency in a region will be affected by the innovation efficiency in neighboring regions, and the regions with high efficiency value tend to cluster in space, while the regions with low efficiency value tend to cluster. 
    Thirdly, from the estimation results of spatial Doberman model, we can see that the inflow and outflow of R&D talents and R&D capital between regions and the spatial spillover effect of R&D capital on innovation efficiency are significantly different. The inflow of R&D talents will promote regional innovation efficiency through direct effect and spatial spillover effect, and the outflow of R&D talents will inhibit the improvement of innovation efficiency, and the inhibition effect of the latter is more than twice of that of the former, that is to say, attracting R&D talents inflow is very important to improve innovation efficiency, but retaining talents, reducing or avoiding R&D talents loss are more critical; R&D capital inflow or "market loss". The "crowding out effect" between government R&D support and enterprise R&D investment has a direct negative impact on innovation efficiency, but it mainly promotes regional innovation efficiency through spatial spillover effect. R&D capital outflow will weaken regional innovation efficiency from both direct effect and spatial spillover effect. 
    Finally, increasing government support and human capital will improve the efficiency of regional innovation. Infrastructure construction is not perfect, which cannot play its due role in promoting the efficiency of innovation. Industrial structure does not play a positive role in the efficiency of regional innovation. Therefore, in order to promote the innovation driven strategy in an all-round way at this stage, we should make full use of the comprehensive implementation of supply side structural reform, start from the supply side, vigorously develop scientific and technological innovation, and change the regional economic development mode from the factor input driven to the scientific and technological innovation driven. 
    Firstly, we need to break down the institutional barriers between regions and stimulate the leading role of the market. Break down the institutional barriers between regions, especially the institutional mechanism that is not conducive to the provincial flow of R&D elements, stimulate the leading role of the market in the rational allocation of resources, take different measures for different R&D elements, reasonably and efficiently guide the harmonious and orderly flow of R&D elements among regions, and expand the spatial spillover radius of R&D element flow. 
    Secondly, give full play to the government′s guiding role and make precise policies for different R&D elements. For R&D talents, it is necessary to improve the salary, welfare and working environment, introduce preferential policies such as zero threshold settlement of highly educated personnel, college students′ entrepreneurial loan support, etc., focus on solving the rigid demand for housing and household registration of knowledge-based talents, accelerate the interconnection between regions with different economic development degrees, and enhance the absorption capacity of R&D talents in regions with insufficient innovation and development capabilities. For R&D capital, local governments should actively promote economic deleveraging, prevent and resolve financial risks, increase equity financing, and give full play to the role of capital market and various financial institutions. 
    Thirdly, fully tap the positive effect of auxiliary elements. Encourage all regions to strengthen the infrastructure construction, promote the transformation and upgrading of industrial structure, attach importance to the cultivation of human capital, fully consider the spatial connection of innovation activities, establish the innovation resource sharing mechanism between adjacent regions, and enhance the interregional exchange and cooperation of innovation resources, so as to comprehensively and efficiently improve the efficiency of regional innovation.

Key words: R&D elements flow, spatial spillover effect, innovation efficiency, Gravity Model, Spatial Durbin Model