A New Endogenous Direction Selection Mechanism for the Direction Distance Function Method Applied to Different Economic–Environmental Development Modes

As a direction selection in the direction distance function (DDF), endogenous DDF can accurately reflect the numerical characteristics of inputs/outputs, but it is difficult to effectively popularize. And it is also difficult to effectively combine with reality. To solve those problems, this paper introduces slack variables to construct a new endogenous direction-setting mechanism, which makes the endogenous model have the conditions to be popularized. Based on the original endogenous DDF, we consider environmental concern, economic concern, coordinated development, and priority development, and then construct six new extended DDF models with slack variables. Based on priority development, we further propose six new extended DDF models. These new extended models can not only realize the complete internalization of direction determination but also overcome the limitations of traditional endogenous models. Combined with the actual case, the emission reduction potential of different areas is revealed, and the improved path is proposed. The results show that the new extended DDF models effectively reflect the different development modes of carbon emissions, and different development modes have a significant impact on emission reduction potential. In addition, compared with economic concern and priority development, coordinated development and environmental concern are most beneficial to carbon emission reduction, but the development mode of environmental concern can better reveal the improved path of environmental development.