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 Chinas regions.
