Analyze agricultural efficiency and influencing factors base on the three-stage DEA model and Malmquist index

Agriculture is an industry highly sensitive to geographical environments and their variations. Thus, geographical environments and variations also exert significant impacts on agricultural efficiency. Meanwhile, enhancing agricultural production efficiency is of paramount importance for ensuring food security and promoting sustainable rural development. This study employs a robust three-stage Data Envelopment Analysis (DEA) framework integrated with the Malmquist index to evaluate the agricultural efficiency of 16 cities in Anhui Province, China. By utilizing panel data spanning 2017 to 2021, the research systematically decomposes efficiency into pure technical, scale, and environment-adjusted components. Specifically, in the second stage, stochastic frontier analysis (SFA) is applied to isolate input slack variables influenced by external factors, including irrigation water consumption, rural household disposable income, and industrialization level, thereby refining DEA estimates to reflect true production efficiency. The findings reveal that after environmental adjustment, the average comprehensive efficiency increases from 0.827 in the first stage to 0.835 in the third stage, highlighting overestimation of efficiency in cities such as Bengbu, where the comprehensive technical efficiency (Crste) declines from 1.000 to 0.977, and underestimation in regions like Suzhou, where it rises from 0.890 to 1.000. Environmental factors exhibit heterogeneous impacts: rural disposable income is significantly negatively correlated with input slack at the 0.01 level, indicating that higher income motivates labor participation and planting expansion; industrialization is significantly positively correlated with input slack at the 0.01 level, suggesting that industrial development may crowd out agricultural resources. Irrigation water use demonstrates a geographic gradient, with higher consumption in rice-growing areas in the south than in wheat-growing areas in the north. Dynamic analysis shows that total factor productivity (TFP) grows at an average annual rate of 3.1 percent from 2017 to 2021, primarily driven by technological progress with an index of 1.017 (increased by 1.7%), while pure technical efficiency chang (pech) with an index of 1.004 (increased by 0.4%) and scale efficiency chang (sech) with an index of 1.010 make limited contributions. TFP peaks at 1.157 (increased by 15.7%) in 2019 and declines to 0.978 (decreased by 2.2%) from 2020 to 2021 due to global economic slowdowns. These findings lay the foundation for regional and national agricultural management initiatives and policies to enhance agricultural efficiency.