The research team, led by economists at Quanzhou Normal University and Fujian Agriculture and Forestry University, built their analysis on marginal productivity theory, a cornerstone of neoclassical economics first formalised by John Bates Clark in the late nineteenth century. The theory holds that the value of any production factor is determined by its marginal contribution to output. Rather than treating farm emissions purely as an undesirable by-product, the researchers modelled them as an implicit input, one that arrives bundled with fertiliser, diesel, machinery and livestock. Cutting emissions, on this view, means cutting something the production system currently relies on, and the foregone output is the opportunity cost of abatement.

To quantify that cost, the team constructed a transcendental logarithmic, or translog, production function, a flexible functional form that allows the substitution elasticities between capital, labour and carbon emissions to vary, unlike the restrictive Cobb-Douglas specification. Agricultural gross output value served as the dependent variable, with capital stock, labour input and carbon emissions as explanatory factors, plus urbanisation rate and rural per capita income as controls. Because the quadratic and interaction terms in a translog model generate severe multicollinearity, the authors turned to ridge regression, a biased estimation technique that trades a small amount of unbiasedness for a substantial reduction in estimator variance. The optimal ridge parameter was determined to be 0.02, at which point all coefficients were significant and the model achieved an R-squared of 0.939.

The emission accounting itself drew on IPCC standard conversion factors applied to nine agricultural carbon sources, spanning fertilisers, agrochemicals, plastic film, agricultural diesel, irrigation, tillage and enteric fermentation and manure from cattle and sheep. Output values were deflated to constant prices using a provincial agricultural price index. Notably, methane from flooded rice paddies and open-field straw burning were excluded because prefecture-level activity data were unavailable, meaning the estimated emissions represent a lower bound on Fujian’s true agricultural greenhouse gas fluxes.

The headline finding is stark: the provincial average shadow price of agricultural carbon emissions rose by 16.9 percent in 2023 compared with 2010, with the upward trend statistically significant and even accelerating in the latter half of the study period for most cities. In plain terms, each tonne of avoided farm emissions now costs Fujian’s agricultural economy more output than it did a decade ago. The authors attribute this to technological progress and capital accumulation, which raise the output efficiency of every unit of carbon emitted, and therefore raise the economic value sacrificed when emissions are curtailed.

Regional disparities proved equally striking. Zhangzhou recorded the highest mean shadow price at 6.72, followed by Fuzhou at 6.27 and Nanping at 6.08, while Xiamen sat at the bottom with 3.94 and Putian at 5.28. A dual spatial pattern emerged, with higher values in the northwestern inland areas and lower values along the southeastern coast, a gap that widened over time. Zhangzhou is an interesting outlier: despite its coastal location, its extensive agricultural production methods yield high marginal output per unit of carbon, pushing abatement costs up. Xiamen’s tiny agricultural sector, less than one percent of city output, explains its persistently low shadow price.

Robustness checks broadly supported the core results. A stochastic frontier analysis re-estimated the production function and confirmed the significantly positive marginal contribution of carbon emissions to output, though the capital coefficient flipped negative, which the authors attribute to diminishing returns and structural mismatch from land fragmentation in Fujian’s small-scale farming. The estimated technical inefficiency variance was effectively zero, collapsing the frontier model to ordinary least squares, so shadow prices were derived solely from the ridge-regularised baseline. Excluding the pandemic years 2020 and 2021 left the carbon coefficient virtually unchanged at 0.589 versus 0.590, indicating the findings are not an artefact of COVID-era disruptions.

The policy implications are considerable. China has pledged a carbon peak by 2030 and carbon neutrality by 2060, and its Implementation Plan for Agricultural and Rural Emission Reduction and Carbon Sequestration makes low-carbon agricultural transformation a binding constraint. The study argues that uniform abatement targets would be economically inefficient. High-shadow-price regions such as Zhangzhou, Fuzhou and Nanping should prioritise efficiency-enhancement pathways, including precision fertilisation, water-saving irrigation, new energy machinery and forestry carbon sink programmes that offset abatement costs, while low-shadow-price regions like Xiamen could pursue total-emission controls and industrial restructuring at minimal economic sacrifice. Carbon trading or transfer mechanisms between the two groups could balance efficiency and equity.

The authors are careful to flag their limitations. The carbon inventory excludes quantitatively significant methane sources, the shadow prices rest on a single modelling framework in a small nine-city sample, and the findings cannot be extrapolated directly to provinces with fundamentally different agricultural systems, such as the mechanised grain belts of northeast China. Nor do the statistical tests establish causal links between industrial structure, technology and the observed regional cost differences. Still, by converting an abstract climate goal into concrete, spatially differentiated numbers, the study offers something policymakers rarely have: a price list for going green, city by city, that shows exactly where each tonne of abatement will hurt the most.

Subject of Research: Estimation of agricultural carbon abatement costs via a marginal-productivity-based production-input model in Fujian Province, China

Article Title: Estimation of agricultural carbon abatement costs using a marginal-productivity-based production-input model: evidence from Fujian Province, China

Article References: Ye, J., Xie, R., Quan, Q., Xie, F., Li, H., Lin, K., & Yang, J. (2026). Estimation of agricultural carbon abatement costs using a marginal-productivity-based production-input model: evidence from Fujian Province, China. Frontiers in Sustainable Food Systems, 10, Article 1953158. https://doi.org/10.3389/fsufs.2026.1953158

Image Credits: AI Generated

DOI: 10.3389/fsufs.2026.1953158

Keywords: agricultural carbon emissions, shadow price, carbon abatement cost, Fujian Province, marginal productivity, translog production function, ridge regression, low-carbon agriculture, China, climate policy, Estimation, agricultural