Abstract This paper designs a coupled mechanism model of financial technology innovation and economic growth, aiming to analyze the impact path of technology finance and technological progress on economic development. Endogenous economic growth theory is adopted, with technological progress as an exogenous variable, and inputs of production factors and products are considered. The growth rate of capital accumulation is calculated using fuzzy principles taken into account from the likelihood distribution under the assumption that the output function is in generalized form. The value of the distance function is calculated considering the orientation efficiency to ensure profit maximization. After eliminating the effect of different magnitudes, the decision degree decomposition is clarified using the Marquist index. The decision unit boundary degrees are reassembled when the information contribution ratio is scaled up by a multiple. Production relative efficiency change index. According to the findings of the economic impact analysis, the eastern financial institutions’ loan growth rate is stable, the entropy index is steadily increasing, and the p-value for the regression coefficient of science and technology finance is less than 0.02. The standard deviation of regional economic growth variables is 1.0209. Consequently, the coupling mechanism model of financial innovation in science and technology and economic growth can encourage investment in such innovation, shorten the technological innovation cycle to speed up the transformation of outcomes and achieve high-quality economic development.
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