A Network Bounded Adjusted Measure for Assessing the Efficiency of Agricultural and Pastoral Systems with Shared Factors and Undesirable Outputs

The acts of assessing the efficiency of agricultural and pastoral systems and improving their production levels have profound implications for the sustainable development of the agricultural economy. Agricultural and pastoral systems are composed of agricultural sub-systems and pastoral sub-systems, which encompass both the production stage and the sales stage. These two sub-systems include shared factors and undesirable outputs, the latter of which refer to by-products such as CO2 emissions, among others. These factors create significant challenges in assessing the efficiency of agricultural and pastoral systems. To address this issue, this study first proposes divisional system network bounded adjusted measure (BAM) models that consider shared factors and undesirable outputs for assessing the efficiency of agricultural sub-systems and pastoral sub-systems. Subsequently, an overall efficiency model for evaluating the efficiency of agricultural and pastoral systems is developed. The new method is applied to evaluate the efficiency of agricultural and pastoral systems across 30 provinces and cities in China. To explore the impact of undesirable outputs, the efficiency that ignores undesirable outputs is compared with our method. The results indicate that efficiency may be misestimated when ignoring undesirable outputs. Additionally, efficiency under different conditions of intermediate products is also computed, revealing that efficiency under the fixed link of intermediate products tends to be overestimated compared to the free link method we used.