The inverted U-shaped relationship between Pig Farming Scale and crop-livestock nutrient matching: evidence from China

Large-scale livestock farming improves production efficiency but may increase environmental pressure by disrupting the balance between livestock manure nutrient supply and cropland nutrient demand. However, the relationship between Pig Farming Scale (scale) and crop–livestock nutrient matching, as measured by the Crop–Livestock Nutrient Matching Index (CNMI), remains insufficiently understood. Using panel data from 29 provincial-level administrative regions in China from 2007 to 2022, this study measures CNMI based on soil nitrogen balance theory and employs a two-way fixed-effects model, subgroup regression and moderation analysis. The results show, first, a significant inverted U-shaped relationship between scale and CNMI, with a turning point at 50.02%. This suggests that the effect of scale on CNMI is nonlinear. To the left of the turning point, the scale effect is relatively dominant; to the right, land carrying-capacity constraints may become more binding, crowding effects may emerge, and the risk of nutrient imbalance may increase. Second, the effect of scale is heterogeneous across different farming-size groups. In the 50–499 head group, scale1 is significantly positively associated with CNMI. In the 500–999 head group, the relationship is significantly inverted U-shaped. In the 1000-head-and-above group, the effect is not statistically significant. Third, Land Transfer Rate (LTR) moderates the inverted U-shaped relationship between scale and CNMI mainly by shifting the turning point rather than significantly changing the curvature, shifting the estimated turning point from 50.02% to 27.57%. These findings support nutrient management, moderate-scale pig farming compatible with land carrying capacity, and improved crop–livestock resource allocation.