Environmental costs should be taken into account when measuring the achievements of China's agricultural development, since the long-term extensive development of agriculture has caused huge environmental pollution. This study took agricultural carbon emissions as an undesired output to estimate the agricultural development efficiency in 31 provinces of China from 1998 to 2016, based on the green total factor productivity, as assessed by the slacks-based measure directional distance function and constructing the global Malmquist-Luenberger index. We measured agricultural carbon emissions in terms of five aspects: agricultural materials, rice planting, soil, livestock and poultry farming, and straw burning, and then compared the green total factor productivity index and the total factor productivity index. The study came to the following conclusions: (1) the green technology efficiency change was smaller than the technology efficiency change at first, but the gap between them is narrowing with time, such that the former is now larger than the latter; (2) the green technology efficiency was in a declining state and the green technology progress was increasing, promoting the green total factor productivity growth, from 1998 to 2016; and (3) China's agricultural green total factor productivity increased by 4.2% annually in the east, 3.4% annually in the central region, and 2.5% annually in the west.
Keywords: agricultural carbon emissions; carbon sources; green total factor productivity; spatial correlation; spatio-temporal differentiation; time evolution.