Various pollutants can cause serious health problems. One of these pollutants is sulfur dioxide which is associated with respiratory problems in humans. In this study, two-stage DEA method is used to estimate the efficiencies of 23 countries for the time period 1990–2017, using capital, labor, and energy consumption as inputs, GDP as a desirable intermediate which is going out of the system, and sulfur oxides as an undesirable intermediate and respiratory disease deaths as an undesirable output. The results showed Iceland, Luxembourg, and New Zealand as the most overall efficient countries in the time period 1990–2017. Previous works have used the additive Chen et al. (2009) two-stage DEA model in order to handle undesirable variables. The contribution of this study is the use of a modified multiplicative Kao and Hwang (2008) two-stage DEA model under the existence of undesirable variables.

各种污染物会导致严重的健康问题。这些污染物之一是二氧化硫，它与人类的呼吸系统疾病有关。在这项研究中，采用两阶段DEA方法估算了1990-2017年期间23个国家的效率，其中使用了资本，劳动力和能源消耗作为输入，GDP作为了系统中理想的中间产品，硫氧化物作为不希望的中间产物，而呼吸道疾病的死亡则作为不希望的产物。结果显示，冰岛，卢森堡和新西兰是1990-2017年期间整体效率最高的国家。先前的工作使用了添加剂Chen等。（2009）两阶段DEA模型，以处理不良变量。