An extended-directional mix-efficiency measure: performance evaluation of OECD countries considering NetZero

Conventional data envelopment analysis (DEA) models make the assumption of controllable inputs and desirable outputs. However, in many real-world applications, there are two major issues facing the management of decision-making units. The first one is how to deal with uncontrollable inputs whose levels are determined by exogenous fixed factors. The second is how to deal with undesirable outputs that are accompanied by desirable outputs. The effect of the operating environment is frequently captured by uncontrollable inputs and undesirable outputs. The modulation of these two factors into a directional DEA model is still in its infancy in the DEA literature. This paper proposes new directional mix-efficiency measure and slacks-based measure models. These two efficiency models are proposed in the context of uncontrollable inputs and undesirable outputs. The new metric looks at how well the input and/or output mix should change to achieve a fully efficient status by decreasing controllable inputs and undesirable outputs and/or increasing desirable outputs while keeping uncontrollable inputs constant. The new mix-efficiency measure is based on the directional distance function and the slacks-based measure. The usefulness and applicability of the proposed models are assessed by measuring the eco-efficiency of the Organization for Economic Co-Operation and Development (OECD) countries. The aim of the application is to measure efficiency in the context of NetZero, with a specific focus on reducing CO₂ emissions. The findings reveal that six countries—France, Luxembourg, Germany, Norway, Sweden, and the UK—have achieved eco-efficiency; therefore, these countries function in the constant returns-to-scale (CRS) region.