A wide variety of footprint concepts is proposed in the scientific literature giving rise to a selection problem. The objective of this paper is to provide an axiomatic foundation to the concept of ecological footprint indices, in particular carbon and energy footprints. For this purpose, we define five axioms representing general properties which any ecological footprint measure should fulfill. It can be shown that there exists a unique index which is characterized by the given set of axioms. Its functional form is determined, and an economic interpretation is given. The most prominent empirical application is discussed. We find that the proposed index as a generalization of more specific indices like carbon and energy footprint indices may confirm some important issues discussed in the literature. First, it incorporates a trade component indicating the ecological footprint of economic activities embodied in the trade pattern of a country or region. Moreover, the productivity of land use in production as a means to mitigate the pressure on the ecological system is reflected. But, most importantly, from a methodological point of view, there is no longer the need for designing ecological footprint indices ad hoc, in particular for the sake of empirical application.

中文翻译：

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关于碳和能源足迹的公理基础

在科学文献中提出了各种各样的足迹概念，这引起选择问题。本文的目的是为生态足迹指数，特别是碳和能源足迹的概念提供公理基础。为此，我们定义了五个公理，这些公理代表任何生态足迹措施都应满足的一般特性。可以证明，存在一个由给定公理集表征的唯一索引。确定其功能形式，并给出经济解释。讨论了最突出的经验应用。我们发现，拟议的指数是对更具体的指数（如碳和能源足迹指数）的概括，可以证实文献中讨论的一些重要问题。第一，它包含一个贸易组件，该组件指示一个国家或地区的贸易模式所体现的经济活动的生态足迹。此外，反映了生产中土地使用的生产力，作为减轻生态系统压力的一种手段。但是，最重要的是，从方法论的角度来看，不再需要特别设计用于生态应用的生态足迹指数。