The economic and social environment is constantly changing, the government’s economic management functions are facing transformation, and the exploration and innovation of the construction of local government economic management performance system is necessary. This paper takes fairness and efficiency as the basic value orientation, selects key indicators from multiple dimensions, and constructs a set of scientific and feasible local government economic management performance evaluation indicators. Twenty provinces in China are selected as research objects, and the entropy method is adopted to determine the weights of each index, combined with the TOPSIS method to make a horizontal comparison of different provinces. And the kernel density estimation method and convergence model are used to analyze the dynamic evolution characteristics and convergence characteristics of the economic management performance level of the Chinese government. The experimental results show that although the average value of the Chinese government’s economic management performance composite score has increased by 0.118 during the period of 2016-2021, there are still some differences in the government’s economic management performance level in different provinces. Except for the Northeast region, all other regions in China have \(sigma\) convergence and conditional \(beta\) convergence. The research in this paper provides a scientific basis for the government to formulate targeted regional economic management strategies and helps to promote the coordinated development of regional economy.
