A Two Stage Data Envelopment Analysis Model With Feedback And Fixed Sum Undesirable Outputs: An Empirical Study Of Provincial Carbon Emissions In China

Data Envelopment Analysis is a pivotal method for evaluating the efficiency of multi-input and multi-output systems. The traditional DEA assumes that the output levels of all decision making units can be adjusted freely. However, in practice, there often exists some constraints such as feedback mechanisms and fixed-sum undesirable outputs, rendering the adjustment of output levels among DMUs no longer satisfying the assumption of independence. Given this, it is necessary to construct a two-stage DEA model with feedback and fixed‑sum undesirable outputs, along with its substage efficiency decomposition model. The Generalized Equilibrium Efficient Frontier DEA method is employed for efficiency evaluation. Furthermore, the proposed method is applied to assess provincial carbon emission efficiency in China, demonstrating its validity and practicality. This research reveals that: 1. Compared to conventional models, the GEEFDEA approach with feedback and fixed-sum undesirable outputs significantly enhances carbon emission efficiency. Especially, regions with high carbon efficiency are mainly located in the eastern and western of China. 2. The substage efficiency decomposition model answers the question of how carbon emission credits should be adjusted at each stage. In the energy production stage, provinces requiring increased emissions are mainly developed eastern regions and underdeveloped western areas, while those needing reductions are predominantly heavy industrial or resource-dependent provinces. In the energy utilization stage, the provinces that need to increase carbon emissions are mainly in the economically active regions, and those that need to reduce carbon emissions are mainly in the provinces with high-emission industries. This research provides critical decision-making insights for enhancing carbon emission efficiency across China’s regions.