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Over recent decades, China's economy has continued to develop steadily and rapidly, contributing to a large environmental cost. Therefore, many researchers propose various methods to evaluate environmental efficiency to deal with these serious issues accurately. This paper is the first to evaluate environmental efficiency using a model featuring not only a parallel structure with three component processes (primary, secondary, and tertiary industries) in the first stage but also a sewage treatment process in the second stage. Simultaneously, we propose radial but also nonradial versions of the Environmental Multiple Variable Return to Scale (EMVRS) model. These two models both consider shared inputs as well as shared outputs, and the proportion of the shared inputs and shared outputs utilized in each component process is assumed to be unknown. Additionally, we further analyze the factors influencing environmental efficiency by utilizing the Tobit model. The results when EMVRS is applied to Chinese provinces can be divided into 3 parts: (1) Most provinces do not purify wastewater appropriately contributing to the bad environmental efficiency. (2) The efficiency values of the three industry types are similar or identical to each other in most provinces. (3) The population of people employed negatively impacts environmental efficiency. [ABSTRACT FROM AUTHOR]

• DEA was applied to assess the environmental efficiency of EU countries. • Fixed environmental cost allocation is considered at the EU level. • Three novel decision goals are proposed. • Policy measures at EU and each member are recommended. Reasonably measure the environmental efficiency is a significant step towards a greener European Union (EU). This paper proposes several data envelopment analysis (DEA) approaches to evaluate the environmental efficiency of EU countries, considering the allocation of fixed environmental costs and three different decision objectives for each member state. Empirical results for the 28 EU member states from 2013 to 2019 show that the efficiency scores of each member remained broadly stable. Spearman's analysis indicates that the efficiency ranking under economic priority and win–win policy is significantly positively correlated, and the ranking under environment priority is significantly negatively correlated with the rankings under the other two policies. The EU as a whole is most efficient under a win–win strategy, but there are significant differences among member states. Member states that joined the EU earlier have higher efficiency values under economic priority. These results can help the EU and Member states understand strengths and weaknesses and implement appropriate policy measures. [ABSTRACT FROM AUTHOR]