Eco-Efficiency Under Synergistic Carbon and Pollution Reduction: Identifying Development States in China’s Beef Cattle Sector Using Unsupervised Machine Learning

Reconciling livestock supply security with synergistic reductions in carbon emissions and environmental pollution is a major governance challenge for China’s beef cattle sector, as provincial production systems differ substantially in resource endowments, production organization, and upgrading capacity. Using a balanced panel of 17 major beef cattle-producing provinces from 2010 to 2023, this study develops a state-based framework to diagnose provincial heterogeneity. We first estimate provincial eco-efficiency using a slack-based measure (SBM) model with undesirable outputs, which jointly accounts for desirable output, greenhouse gas (GHG) emissions, and pollutant discharges. We then apply K-means clustering, an unsupervised machine learning method, to a multidimensional feature space covering eco-efficiency, environmental intensity, input structure, production scale, sectoral specialization, and the agricultural fiscal expenditure context to identify empirically coherent development states. The results reveal four distinct states: factor-intensive, moderate-scale eco-efficiency, scale-driven low-intensity, and extensive high-pressure. The four states exhibit systematically different production–environment configurations and structural characteristics, demonstrating substantial heterogeneity across provincial beef cattle systems. The resulting typology provides a descriptive basis for considering differentiated, state-informed policy directions while recognizing that the effects of specific policy instruments require further evaluation.