Environmental Omission and the Measurement of Agricultural Productivity in China: Evidence from a Meta-Frontier Global Malmquist–Luenberger Framework

Conventional agricultural productivity assessments that exclude carbon emissions may provide an incomplete representation of environmental performance, particularly when production technologies differ across regions. This study examines how excluding agricultural carbon emissions changes measured productivity growth in Chinese agriculture. Using panel data for 30 provinces from 2012 to 2021, we apply a Global Malmquist–Luenberger (GML) framework using regional group frontiers and a national meta-frontier. Productivity is estimated with and without carbon emissions and decomposed into efficiency change (EFFCH) and global technology-gap change (GTC). Regional technology gap ratios (TGRs) are also examined. Under constant returns to scale, the mean group-frontier GML index increases from 1.011 to 1.012 when emissions are excluded, while the meta-frontier index rises from 1.014 to 1.025. However, the direction of the difference varies across provinces and years. Under the meta-frontier, excluding emissions increases mean EFFCH but reduces mean GTC. The Central region records a lower emissions-inclusive TGR than the Eastern and Western regions, indicating a larger measured technology gap. Sensitivity analyses using variable returns to scale, alternative input specifications, and leave-one-province-out estimation show that some differences depend on modeling choices. These results demonstrate the importance of environmental specification and reference technology in interpreting agricultural productivity growth.