This paper studies the mechanism of interaction between cultural industry and regional economic growth, taking Quanzhou as the research object, and adopting the research method of grey relational analysis. On the basis of understanding the development status of Quanzhou's cultural industry and its development opportunities under the background of the "One Belt and One Road", a gray correlation analysis model was created to study the internal mechanism of cultural industries affecting Quanzhou's economy, and its gray correlation degree was calculated, and the impact on Quanzhou's economy was calculated. The main factors are investment in the cultural industry and the number of employees. On this basis, the elasticity analysis of Quanzhou's economy and the three major industries is made, and its sensitivity to economic changes is analyzed, and the conclusion is drawn that the cultural industry drives Quanzhou's economic growth. Based on the conclusions of empirical analysis, discuss how to optimize the safeguard measures of cultural industry development under the background of "One Belt and One Road", so as to further promote the stimulating effect of cultural industry on Quanzhou's economy.
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