Green total factor productivity growth of China's agricultural sector: A new metafrontier biennial Malmquist-Luenberger productivity index

China has made substantial advances in agricultural development, however, its earlier reliance on extensive farming practices has placed considerable pressure on extensive farming practices has placed considerable pressure on the ecological environment. Improving China's agricultural green total factor productivity (GTFP) is essential for alleviating ecological pressures and promoting sustainable and high-quality agricultural development. This study proposes a novel metafrontier biennial Malmquist-Luenberger productivity index (MLPI) by developing a non-oriented biennial directional distance function that incorporates undesirable outputs and integrating it with the MLPI framework under a metafrontier setting. The new index expresses GTFP change as an output-input ratio form, which aligns with the definition of productivity, and it has the advantages of accounting for technological heterogeneity, avoiding infeasible solutions, maintaining computational simplicity, and accommodating technology regression. Using this method, we measure and analyze China's agricultural GTFP growth between 2005 and 2021. The empirical results show that agricultural GTFP experienced sustained growth, with an average annual rate of 6.66%, driven primarily by technological progress. GTFP evolution exhibited clear stage-wise patterns, i.e., rapid growth during 2005–2011, a slowdown in 2011–2016 due to stricter environmental regulations, and a rebound after 2016. Additionally, significant regional disparities are observed, with the western region achieving the fastest agricultural GTFP growth, followed by the eastern and central regions. Regional differences arise mainly from gaps in green agricultural technological innovation. These findings underscore the importance of accelerating green technological innovation, enhancing innovation capacity, and strengthening talent and infrastructure to promote balanced and sustainable agricultural development in China.